a:B where a is included because it is referenced by all b in B af: af.divisor_function af.bernoulli_numbers: cmf.eisenstein af.divisor_function: cmf.eisenstein af.multiplicative: af.divisor_function ag.abelian_variety: ag.base_field, ag.complex_multiplication, ag.endomorphism_algebra, ag.endomorphism_ring, ag.geom_simple, ag.jacobian, ag.mordell_weil, ag.simple, av.isogeny, av.simple, av.twist, ec.bsdconjecture, ec.endomorphism, ec.endomorphism_ring, ec.geom_endomorphism_ring, ec.mordell_weil_group, ec.q.bsdconjecture, ec.q.endomorphism_ring, nf.weil_polynomial, st_group.definition ag.affine_space: ag.variety ag.base_change: ag.minimal_field, av.twist ag.base_field: ec.isogeny ag.complex_multiplication: ec.complex_multiplication ag.curve: ag.curve.smooth, ag.hyperelliptic_curve, ag.quotient_curve, ec, g2c.aut_grp ag.curve.genus: ag.hyperelliptic_curve, ag.minimal_field, ec, g2c.minimal_equation ag.curve.smooth: ec, ec.discriminant, ec.good_reduction, g2c.minimal_equation, modcurve ag.dimension: ag.complex_multiplication, ag.mordell_weil, st_group.definition ag.endomorphism_algebra: ag.complex_multiplication ag.endomorphism_ring: ag.complex_multiplication, ag.endomorphism_algebra, ag.geom_endomorphism_ring, ec.endomorphism, ec.endomorphism_ring, ec.q.endomorphism_ring ag.geom_endomorphism_ring: ec.geom_endomorphism_ring ag.geom_simple: ag.complex_multiplication ag.hyperelliptic_curve: g2c.g2curve, g2c.minimal_equation ag.irreducible: ag.dimension ag.jacobian: g2c.good_reduction ag.minimal_field: ag.base_field ag.mordell_weil: ec.mordell_weil_group, ec.q.analytic_rank ag.projective_space: ag.variety ag.quotient_curve: modcurve ag.riemann_surface: ag.curve.genus ag.simple: ag.geom_simple ag.singular_point: ag.curve.smooth ag.variety: ag.abelian_variety, ag.base_change, ag.curve, ag.dimension, ag.irreducible, ag.minimal_field, ag.quotient_curve, g2c.good_reduction, nf.weil_height alg.binary_operation: alg.binary_operation.associative, alg.binary_operation.commutative, alg.binary_operation.identity, alg.binary_operation.inverse, group, group.abelian, group.subgroup, group.subgroup.normal, ring alg.binary_operation.associative: group, ring alg.binary_operation.commutative: group.abelian, ring alg.binary_operation.identity: alg.binary_operation.inverse, group, group.subgroup, ring alg.binary_operation.inverse: group, group.subgroup, ring.field alg.symplectic_isomorphism: modcurve.xn artin: artin.conductor, artin.number_field, artin.parity, artin.ramified_primes, artin.unramified_primes, cmf.galois_representation, st_group.definition artin.conductor: cmf.galois_representation artin.number_field: artin.ramified_primes, artin.unramified_primes artin.parity: cmf.galois_representation artin.ramified_primes: artin.unramified_primes artin.unramified_primes: artin.conductor av.isogeny: av.tate_module, ec.isogeny av.simple: nf.weil_polynomial av.tate_module: ec.padic_tate_module av.twist: ec.twists character.dirichlet: character.dirichlet.conductor, character.dirichlet.galois_orbit, character.dirichlet.galois_orbit_index, character.dirichlet.galois_orbit_label, character.dirichlet.induce, character.dirichlet.minimal, character.dirichlet.order, character.dirichlet.primitive, character.dirichlet.principal, cmf, cmf.character, cmf.cusp_form, cmf.eisenstein_form, cmf.eisenstein_label, cmf.eisenstein_newspace, cmf.eisenstein_series, cmf.embedding, cmf.hecke_operator, cmf.inner_twist, cmf.inner_twist_count, cmf.inner_twist_multiplicity, cmf.label, cmf.labels, cmf.newspace, cmf.self_twist, cmf.shimura_correspondence, cmf.subspaces, cmf.twist, nf.dirichlet_group character.dirichlet.conductor: character.dirichlet.minimal, character.dirichlet.primitive, cmf.oldspace, cmf.subspaces, cmf.twist character.dirichlet.galois_orbit: character.dirichlet.galois_orbit_index, character.dirichlet.galois_orbit_label, cmf.eisenstein_label, cmf.inner_twist, cmf.inner_twist_multiplicity, cmf.label, cmf.labels, cmf.twist, cmf.twist_multiplicity character.dirichlet.galois_orbit_index: character.dirichlet.galois_orbit_label character.dirichlet.galois_orbit_label: cmf.eisenstein_label, cmf.embedding_label, cmf.label, cmf.labels character.dirichlet.induce: character.dirichlet.primitive, character.dirichlet.principal, cmf.eisenstein_newspace, cmf.newspace, cmf.oldspace, cmf.subspaces character.dirichlet.minimal: cmf.minimal_twist, cmf.twist_minimal character.dirichlet.modulus: character.dirichlet.galois_orbit, character.dirichlet.galois_orbit_index, character.dirichlet.induce, character.dirichlet.minimal, character.dirichlet.order, character.dirichlet.primitive, character.dirichlet.principal, cmf.eisenstein_newspace, cmf.newspace, cmf.subspaces character.dirichlet.order: character.dirichlet.galois_orbit, character.dirichlet.galois_orbit_index, character.dirichlet.minimal, character.dirichlet.value_field, cmf.self_twist character.dirichlet.primitive: character.dirichlet.minimal, cmf.eisenstein_series, cmf.inner_twist, cmf.oldspace, cmf.self_twist, cmf.twist, cmf.twist_multiplicity character.dirichlet.principal: character.dirichlet.galois_orbit_index, character.dirichlet.minimal, character.dirichlet.order character.dirichlet.value_field: character.dirichlet.galois_orbit, character.dirichlet.galois_orbit_index, cmf.embedding cmf: cmf.bad_prime, cmf.character, cmf.cm_form, cmf.coefficient_ring, cmf.cusp_form, cmf.eisenstein, cmf.eisenstein_form, cmf.eisenstein_newspace, cmf.fouriercoefficients, cmf.fouriercoefficients_mathlib_def, cmf.hecke_operator, cmf.level, cmf.newspace, cmf.oldspace, cmf.q-expansion_mathlib_def, cmf.rm_form, cmf.space, cmf.subspaces, cmf.weight cmf.analytic_rank: cmf.fricke cmf.artin_field: cmf.artin_image, cmf.stark_unit cmf.atkin-lehner: cmf.fricke cmf.bad_prime: cmf.satake_parameters cmf.character: cmf.eisenstein_newspace, cmf.embedding, cmf.maximal, cmf.minimal_twist, cmf.newspace, cmf.oldspace, cmf.satake_parameters, cmf.space, cmf.sturm_bound, cmf.subspaces, cmf.twist_minimal cmf.cm_form: cmf.inner_twist, cmf.sato_tate cmf.coefficient_field: cmf.analytic_rank, cmf.coefficient_ring, cmf.defining_polynomial, cmf.dualform, cmf.eisenstein_label, cmf.embedding, cmf.inner_twist, cmf.inner_twist_count, cmf.label, cmf.labels, cmf.selfdual, cmf.trace_bound, cmf.trace_form cmf.coefficient_ring: cmf.hecke_ring_generators cmf.congruence_subgroup: modcurve, modcurve.xn cmf.cusp_form: cmf.analytic_rank, cmf.atkin-lehner, cmf.coefficient_field, cmf.cusp_form_subspace_mathlib_def, cmf.dualform, cmf.eisenstein_form, cmf.embedding_label, cmf.hecke_operator, cmf.hecke_orbit, cmf.newspace, cmf.oldspace, cmf.petersson_scalar_product, cmf.q-expansion, cmf.selfdual, cmf.space, cmf.subspaces cmf.cusp_form_mathlib_def: cmf.cusp_form cmf.cusp_form_subspace_mathlib_def: cmf.subspaces cmf.dimension: cmf.inner_twist_count, cmf.maximal, cmf.trace_bound, cmf.trace_form cmf.dimension_mathlib_def: cmf.dimension cmf.eisenstein_form: cmf.eisenstein_newspace cmf.eisenstein_newform: cmf.eisenstein_label cmf.eisenstein_newspace: cmf.eisenstein_newform cmf.eisenstein_series: cmf.eisenstein_form, cmf.eisenstein_newspace cmf.embedding: cmf.eisenstein_label, cmf.embedding_label, cmf.inner_twist_multiplicity, cmf.label, cmf.labels cmf.fouriercoefficients: cmf.coefficient_field, cmf.cusp_form, cmf.eisenstein_newform, cmf.newform, cmf.q-expansion, cmf.sturm_bound, cmf.sturm_bound_gamma1 cmf.fricke: cmf.minus_space, cmf.plus_space cmf.galois_conjugate: cmf.galois_orbit, cmf.inner_twist, cmf.twist cmf.galois_orbit: cmf.dimension, cmf.distinguishing_primes, cmf.eisenstein_label, cmf.embedding, cmf.inner_twist, cmf.label, cmf.labels, cmf.maximal, cmf.q-expansion, cmf.trace_bound, cmf.twist, cmf.twist_minimal, cmf.twist_multiplicity cmf.galois_representation: cmf.artin_field, cmf.artin_image, cmf.projective_field, cmf.projective_image, cmf.stark_unit cmf.hecke_operator: cmf.atkin-lehner, cmf.coefficient_field, cmf.coefficient_ring, cmf.decomposition.new.gamma0chi, cmf.distinguishing_primes, cmf.eisenstein_newform, cmf.hecke_orbit, cmf.heckecharpolys, cmf.newform, cmf.satake_parameters cmf.inner_twist: cmf.inner_twist_count, cmf.inner_twist_multiplicity, cmf.nontrivial_twist, cmf.twist, cmf.twist_multiplicity cmf.inner_twist_count: cmf.twist_multiplicity cmf.label: cmf.minimal_twist, cmf.twist_minimal cmf.level: cmf.bad_prime, cmf.eisenstein, cmf.eisenstein_label, cmf.eisenstein_newspace, cmf.embedding_label, cmf.hecke_operator, cmf.hecke_orbit, cmf.label, cmf.labels, cmf.minimal_twist, cmf.newspace, cmf.oldspace, cmf.satake_parameters, cmf.self_twist, cmf.space, cmf.sturm_bound, cmf.sturm_bound_gamma1, cmf.subspaces, cmf.twist_minimal, ec.q.serre_invariants cmf.newform: cmf.analytic_conductor, cmf.artin_field, cmf.artin_image, cmf.coefficient_ring, cmf.decomposition.new.gamma0chi, cmf.dimension, cmf.distinguishing_primes, cmf.dualform, cmf.galois_conjugate, cmf.galois_orbit, cmf.galois_representation, cmf.hecke_ring_generators, cmf.heckecharpolys, cmf.inner_twist, cmf.inner_twist_count, cmf.inner_twist_multiplicity, cmf.label, cmf.maximal, cmf.minimal_twist, cmf.newform_subspace, cmf.projective_field, cmf.projective_image, cmf.q-expansion, cmf.relative_dimension, cmf.satake_parameters, cmf.sato_tate, cmf.self_twist, cmf.selfdual, cmf.space_trace_form, cmf.stark_unit, cmf.sturm_bound, cmf.sturm_bound_gamma1, cmf.trace_bound, cmf.trace_form, cmf.twist, cmf.twist_minimal cmf.newform_subspace: cmf.dimension, cmf.galois_orbit, cmf.heckecharpolys cmf.newspace: cmf.distinguishing_primes, cmf.newform, cmf.newform_subspace, cmf.oldspace, cmf.space_trace_form, cmf.trace_bound, cmf.trace_form cmf.petersson_scalar_product: cmf.eisenstein_form, cmf.hecke_operator, cmf.newspace, cmf.subspaces cmf.petersson_scalar_product_mathlib_def: cmf.petersson_scalar_product cmf.projective_image: cmf.self_twist cmf.q-expansion: cmf.analytic_rank, cmf.dualform, cmf.eisenstein, cmf.embedding, cmf.fouriercoefficients_mathlib_def, cmf.hecke_ring_generators, cmf.selfdual, cmf.trace_bound cmf.q-expansion_mathlib_def: cmf.q-expansion cmf.relative_dimension: cmf.eisenstein_label, cmf.label, cmf.labels cmf.rm_form: cmf.inner_twist cmf.satake_parameters: cmf.satake_angles cmf.self_twist: cmf.cm_form, cmf.inner_twist, cmf.inner_twist_count, cmf.nontrivial_twist, cmf.rm_form cmf.selfdual: cmf.analytic_rank, cmf.dualform cmf.space: cmf.dimension_mathlib_def, cmf.subspaces cmf.space_mathlib_def: cmf, cmf.cusp_form_subspace_mathlib_def, cmf.dimension_mathlib_def, cmf.space cmf.twist: cmf.minimal_twist, cmf.twist_minimal, cmf.twist_multiplicity cmf.twist_minimal: cmf.minimal_twist cmf.weight: cmf.artin_field, cmf.artin_image, cmf.atkin-lehner, cmf.cusp_form, cmf.eisenstein, cmf.eisenstein_form, cmf.eisenstein_label, cmf.eisenstein_newspace, cmf.eisenstein_series, cmf.embedding_label, cmf.galois_representation, cmf.hecke_operator, cmf.inner_twist_count, cmf.label, cmf.labels, cmf.newspace, cmf.oldspace, cmf.projective_field, cmf.projective_image, cmf.satake_parameters, cmf.sato_tate, cmf.self_twist, cmf.space, cmf.stark_unit, cmf.sturm_bound, cmf.sturm_bound_gamma1, cmf.subspaces, ec.q.serre_invariants ec: ag.abelian_variety, ec.additive_reduction, ec.analytic_sha_order, ec.bad_reduction, ec.bsdconjecture, ec.canonical_height, ec.complex_multiplication, ec.conductor, ec.discriminant, ec.endomorphism, ec.endomorphism_ring, ec.galois_rep, ec.galois_rep_modell_image, ec.global_minimal_model, ec.good_ordinary_reduction, ec.good_reduction, ec.good_supersingular_reduction, ec.integral_model, ec.invariants, ec.isogeny, ec.isogeny_class, ec.isogeny_class_degree, ec.isogeny_graph, ec.isogeny_matrix, ec.isomorphism, ec.j_invariant, ec.kodaira_symbol, ec.local_data, ec.local_minimal_discriminant, ec.local_minimal_model, ec.maximal_elladic_galois_rep, ec.maximal_galois_rep, ec.minimal_discriminant, ec.mordell_weil_group, ec.mordell_weil_theorem, ec.multiplicative_reduction, ec.mw_generators, ec.nonsplit_multiplicative_reduction, ec.obstruction_class, ec.period, ec.potential_good_reduction, ec.q.abc_quality, ec.q.analytic_rank, ec.q.analytic_sha_order, ec.q.bsdconjecture, ec.q.canonical_height, ec.q.conductor, ec.q.cremona_label, ec.q.discriminant, ec.q.endomorphism_ring, ec.q.faltings_height, ec.q.faltings_ratio, ec.q.j_invariant, ec.q.lmfdb_label, ec.q.manin_constant, ec.q.minimal_twist, ec.q.modular_degree, ec.q.modular_parametrization, ec.q.naive_height, ec.q.period_lattice, ec.q.regulator, ec.q.semistable, ec.q.special_value, ec.q.szpiro_ratio, ec.q.torsion_growth, ec.q_curve, ec.rank, ec.reduction, ec.reduction_type, ec.regulator, ec.ring, ec.semi_global_minimal_model, ec.semistable, ec.simple_equation, ec.special_value, ec.split_multiplicative_reduction, ec.tamagawa_number, ec.torsion_order, ec.twists, ec.weierstrass_coeffs, modcurve, modcurve.level_structure, st_group.definition ec.additive_reduction: ec.bad_reduction, ec.conductor, ec.q.conductor ec.analytic_sha_order: ec.bsdconjecture, ec.q.bsdconjecture ec.bad_reduction: ec.conductor, ec.q.semistable, ec.reduction, ec.reduction_type, ec.semistable, ec.simple_equation ec.base_change: ec.analytic_sha_order, ec.period, ec.q_curve, ec.regulator, modcurve.level_structure ec.bsdconjecture: ec.special_value ec.canonical_height: ec.q.regulator, ec.regulator ec.complex_multiplication: ec.galois_rep, ec.galois_rep_adelic_image, ec.maximal_elladic_galois_rep, ec.maximal_galois_rep, ec.q.minimal_twist, ec.q_curve ec.conductor: ec.invariants, ec.q.lmfdb_label ec.discriminant: ec.bad_reduction, ec.invariants, ec.j_invariant, ec.local_minimal_model, ec.minimal_discriminant, ec.period, ec.q.discriminant, ec.q.faltings_height, ec.semi_global_minimal_model ec.endomorphism: ec.endomorphism_ring, ec.isogeny, ec.padic_tate_module, ec.q.endomorphism_ring ec.endomorphism_ring: ec.complex_multiplication, ec.geom_endomorphism_ring, ec.invariants, ec.isogeny ec.galois_rep: ec.galois_rep_adelic_image, ec.galois_rep_modell_image, ec.maximal_elladic_galois_rep, ec.maximal_galois_rep, ec.q.serre_invariants, modcurve, modcurve.level_structure ec.geom_endomorphism_ring: ec.complex_multiplication, ec.maximal_elladic_galois_rep, ec.maximal_galois_rep, ec.q.endomorphism_ring ec.global_minimal_model: ec.minimal_discriminant, ec.obstruction_class, ec.period, ec.q.period_lattice ec.good_reduction: ec.conductor, ec.potential_good_reduction, ec.reduction_type, ec.ring, ec.simple_equation, ec.tamagawa_number ec.integral_model: ec.global_minimal_model ec.isogeny: ec.isogeny_class, ec.isogeny_class_degree, ec.isomorphism, ec.q.cremona_label, ec.q.faltings_ratio, ec.q.manin_constant, ec.q_curve, ec.rank ec.isogeny_class: ec.isogeny_class_degree, ec.isogeny_graph, ec.isogeny_matrix, ec.q.cremona_label, ec.q.lmfdb_label, ec.q.minimal_twist, ec.q.optimal, ec.rank ec.isomorphism: ec.j_invariant, ec.q.cremona_label, ec.q.lmfdb_label, ec.weierstrass_isomorphism ec.j_invariant: ec.base_change, ec.complex_multiplication, ec.invariants, ec.potential_good_reduction, ec.q.abc_quality, ec.q.faltings_height, ec.q.minimal_twist, ec.reduction, ec.twists ec.kodaira_symbol: ec.local_data ec.local_minimal_discriminant: ec.minimal_discriminant ec.local_minimal_model: ec.global_minimal_model, ec.kodaira_symbol, ec.local_minimal_discriminant, ec.semi_global_minimal_model ec.minimal_discriminant: ec.invariants, ec.period, ec.q.minimal_twist, ec.q.szpiro_ratio, ec.semi_global_minimal_model ec.mordell_weil_group: ec.analytic_sha_order, ec.canonical_height, ec.mordell_weil_theorem, ec.mw_generators, ec.q.analytic_rank, ec.q.regulator, ec.rank, ec.regulator, ec.torsion_order, ec.torsion_subgroup ec.mordell_weil_theorem: ec.q.bsdconjecture, ec.rank, ec.torsion_order, ec.torsion_subgroup ec.multiplicative_reduction: ec.conductor, ec.q.conductor ec.nonsplit_multiplicative_reduction: ec.bad_reduction, ec.multiplicative_reduction ec.padic_tate_module: ec.galois_rep ec.period: ec.analytic_sha_order, ec.bsdconjecture ec.potential_good_reduction: ec.reduction ec.q: ec.q.optimal ec.q.bsdconjecture: ec.q.special_value ec.q.conductor: ec.q.abc_quality, ec.q.cremona_label, ec.q.lmfdb_label, ec.q.manin_constant, ec.q.minimal_twist, ec.q.optimal, ec.q.szpiro_ratio ec.q.discriminant: ec.q, ec.q.j_invariant, ec.q.period_lattice ec.q.faltings_height: ec.q.faltings_ratio ec.q.j_invariant: ec.q.szpiro_ratio ec.q.minimal_weierstrass_equation: ec.q, ec.q.discriminant, ec.q.kodaira_symbol, ec.q.lmfdb_label, ec.q.real_period, ec.q.reduction_type, ec.simple_equation ec.q.modular_parametrization: ec.q.manin_constant, ec.q.modular_degree ec.q.optimal: ec.q.cremona_label, ec.q.manin_constant ec.q.period_lattice: ec.period, ec.q.faltings_height, ec.q.faltings_ratio ec.q.real_period: ec.q.bsdconjecture, ec.q.period_lattice ec.q.reduction_type: ec.q.kodaira_symbol ec.rank: ec.analytic_sha_order, ec.bsdconjecture, ec.mw_generators, ec.q.bsdconjecture, ec.regulator ec.reduction_type: ec.kodaira_symbol, ec.local_data, ec.q.semistable, ec.reduction, ec.semistable ec.regulator: ec.analytic_sha_order, ec.bsdconjecture, ec.q.bsdconjecture, ec.q.canonical_height ec.ring: modcurve.xn ec.scheme: ec.ring ec.semistable: ec.q.faltings_height, ec.q.manin_constant, ec.reduction ec.split_multiplicative_reduction: ec.bad_reduction, ec.multiplicative_reduction ec.tamagawa_number: ec.analytic_sha_order, ec.bsdconjecture, ec.local_data, ec.q.bsdconjecture ec.torsion_order: ec.q.bsdconjecture ec.torsion_subgroup: ec.analytic_sha_order, ec.bsdconjecture, ec.mw_generators, ec.q.torsion_growth, ec.rank, ec.torsion_order ec.twists: ec.q.minimal_twist ec.weierstrass_coeffs: ec.discriminant, ec.global_minimal_model, ec.integral_model, ec.invariants, ec.j_invariant, ec.local_minimal_model, ec.minimal_discriminant, ec.period, ec.q.j_invariant, ec.q.naive_height, ec.q.period_lattice, ec.q.real_period, ec.weierstrass_isomorphism ec.weierstrass_isomorphism: ec.q.real_period g2c.aut_grp: ag.quotient_curve, ec.twists g2c.discriminant: g2c.g2curve, g2c.minimal_equation g2c.g2curve: g2c.aut_grp g2c.good_reduction: g2c.minimal_equation g2c.minimal_equation: g2c.g2curve gg.galois_group: artin.conductor gl2.borel: ec.galois_rep_modell_image, ec.maximal_galois_rep, gl2.exceptional gl2.cartan: gl2.nonsplit_cartan, gl2.normalizer_cartan, gl2.split_cartan gl2.exceptional: ec.galois_rep_modell_image gl2.index: ec.galois_rep gl2.level: ec.galois_rep, gl2.index, modcurve, modcurve.level_structure gl2.nonsplit_cartan: ec.galois_rep_modell_image, gl2.normalizer_nonsplit_cartan gl2.normalizer_cartan: gl2.exceptional gl2.normalizer_nonsplit_cartan: ec.galois_rep_modell_image, ec.maximal_galois_rep gl2.normalizer_split_cartan: ec.galois_rep_modell_image, ec.maximal_galois_rep gl2.open: ec.galois_rep, ec.galois_rep_adelic_image, gl2.index, gl2.level, modcurve, modcurve.level_structure, modcurve.xn gl2.profinite: gl2.index, gl2.open gl2.split_cartan: ec.galois_rep_modell_image, gl2.normalizer_split_cartan group: group.abelian, group.automorphism, group.characteristic_subgroup, group.coset, group.generators, group.haar_measure, group.homomorphism, group.normal_series, group.order, group.rank, group.subgroup, group.subgroup.normal, group.sylow_subgroup, group.torsion, ring.characteristic, ring.unit group.abelian: ec.analytic_sha_order, ec.mw_generators, group.torsion, ring group.automorphism: group.characteristic_subgroup, group.generators group.characteristic_subgroup: group.frattini_subgroup group.coset: group.subgroup.index, group.subgroup.normal group.frattini_subgroup: group.rank group.fuchsian.cusps: cmf, cmf.cusp_form, cmf.fouriercoefficients, cmf.q-expansion, group.fuchsian.cusps.width group.fuchsian.cusps.width: cmf.fouriercoefficients group.fuchsian.fundamental_domain: cmf.petersson_scalar_product group.galois.absolute: artin, av.tate_module, ec.analytic_sha_order, ec.galois_rep, ec.padic_tate_module group.generators: group.rank group.haar_measure: st_group.definition group.homomorphism: ec.isogeny, group.isomorphism group.isomorphism: group.automorphism group.maximal_subgroup: group.frattini_subgroup group.normal_series: group.presentation group.order: ec.analytic_sha_order, ec.q.analytic_sha_order, group.haar_measure, group.sylow_subgroup group.presentation: group.rank group.rank: ec.q.period_lattice group.sl2z: cmf, cmf.cusp_form, cmf.eisenstein, cmf.eisenstein_form, cmf.level, group.fuchsian.cusps, group.fuchsian.cusps.width, group.fuchsian.fundamental_domain, mf.upper_half_plane group.subgroup: group.characteristic_subgroup, group.coset, group.normal_series, group.subgroup.normal, group.sylow_subgroup, nf.reflex_field, ring.ideal group.subgroup.index: cmf.petersson_scalar_product, ec.q.faltings_ratio group.subgroup.normal: group.frattini_subgroup, group.normal_series group.sylow_subgroup: lf.wild_inertia_group group.torsion: ec.analytic_sha_order lf.automorphism_group: nf.galois_group lf.inertia_group: artin.conductor, lf.wild_inertia_group lf.local_field: lf.maximal_ideal, lf.padic_field, lf.ring_of_integers lf.maximal_ideal: lf.inertia_group, lf.residue_field lf.padic_field: artin.conductor, lf.inertia_group lf.qp: lf.padic_field lf.residue_field: lf.inertia_group lf.ring_of_integers: lf.maximal_ideal, lf.residue_field, nf.padic_completion lf.wild_inertia_group: artin.conductor lfunction: cmf.embedding, cmf.fricke, ec.bsdconjecture, ec.q.analytic_rank, ec.q.bsdconjecture, ec.special_value, lfunction.analytic_rank, lfunction.arithmetic, lfunction.central_point, lfunction.critical_line, lfunction.dual, lfunction.rh lfunction.analytic_rank: cmf.analytic_rank, ec.bsdconjecture lfunction.arithmetic: lfunction.leading_coeff lfunction.central_point: ec.bsdconjecture, ec.q.analytic_rank, ec.q.bsdconjecture, lfunction.analytic_rank, lfunction.leading_coeff lfunction.critical_line: lfunction.central_point lfunction.dirichlet_series: lfunction lfunction.dual: cmf.dualform lfunction.euler_product: lfunction, lfunction.gamma_factor lfunction.functional_equation: cmf.fricke, ec.q.analytic_rank, lfunction, lfunction.central_point, lfunction.critical_line, lfunction.normalization, lfunction.sign lfunction.gamma_factor: lfunction.functional_equation lfunction.leading_coeff: ec.bsdconjecture, ec.special_value lfunction.normalization: ec.q.special_value, ec.special_value lfunction.rh: nf.serre_odlyzko_bound lfunction.self-dual: cmf.selfdual lfunction.sign: ec.q.analytic_rank mf.half_integral_weight.dedekind_eta: cmf.eta_quotient mf.upper_half_plane: cmf, modcurve, modcurve.xn modcurve: ec.galois_rep_adelic_image modcurve.cusps: modcurve modcurve.level_structure: modcurve modcurve.xn: modcurve nf: artin.number_field, cmf.defining_polynomial, cmf.projective_field, cmf.q-expansion, ec.additive_reduction, ec.analytic_sha_order, ec.bad_reduction, ec.bsdconjecture, ec.canonical_height, ec.conductor, ec.galois_rep, ec.galois_rep_modell_image, ec.global_minimal_model, ec.good_ordinary_reduction, ec.good_reduction, ec.good_supersingular_reduction, ec.invariants, ec.isogeny, ec.kodaira_symbol, ec.local_data, ec.local_minimal_discriminant, ec.local_minimal_model, ec.maximal_elladic_galois_rep, ec.maximal_galois_rep, ec.minimal_discriminant, ec.mordell_weil_group, ec.mordell_weil_theorem, ec.multiplicative_reduction, ec.mw_generators, ec.nonsplit_multiplicative_reduction, ec.obstruction_class, ec.period, ec.potential_good_reduction, ec.q.regulator, ec.q.torsion_growth, ec.q_curve, ec.rank, ec.reduction_type, ec.regulator, ec.semi_global_minimal_model, ec.special_value, ec.split_multiplicative_reduction, ec.tamagawa_number, modcurve.level_structure, nf.abelian, nf.abs_discriminant, nf.arithmetically_equivalent, nf.class_number, nf.class_number_formula, nf.cm_field, nf.complex_embedding, nf.conductor, nf.defining_polynomial, nf.discriminant, nf.embedding, nf.fundamental_units, nf.galois_root_discriminant, nf.generator, nf.ideal_class_group, nf.inessential_prime, nf.integral, nf.integral_basis, nf.local_algebra, nf.max_p, nf.maximal_cm_subfield, nf.minimal_polynomial, nf.minimal_sibling, nf.monogenic, nf.monomial_order, nf.narrow_class_group, nf.narrow_class_number, nf.order, nf.padic_completion, nf.place, nf.polredabs, nf.poly_discriminant, nf.prime, nf.radical_discriminant, nf.rank, nf.regulator, nf.relative_class_number, nf.ring_of_integers, nf.root_discriminant, nf.serre_odlyzko_bound, nf.signature, nf.torsion, nf.totally_imaginary, nf.totally_positive, nf.totally_real, nf.unit_group, nf.unit_signature_rank, nf.unramified_prime, nf.weil_height, nf.zk_index, ring.dedekind_domain nf.abelian: nf.conductor, nf.dirichlet_group nf.absolute_value: lf.local_field, lf.maximal_ideal, lf.ring_of_integers, nf.place nf.class_number: ec.complex_multiplication, ec.global_minimal_model, ec.semi_global_minimal_model, nf.class_number_formula, nf.narrow_class_number, nf.relative_class_number nf.cm_field: ag.complex_multiplication, cmf.dualform, cmf.selfdual, nf.maximal_cm_subfield, nf.reflex_field, nf.reflex_reflex_field, nf.relative_class_number, st_group.definition nf.complex_embedding: nf.embedding, nf.place, nf.reflex_field, nf.signature nf.conductor: nf.dirichlet_group nf.defining_polynomial: nf.generator nf.degree: ag.complex_multiplication, cmf.galois_conjugate, ec.q.torsion_growth, ec.regulator, nf, nf.arithmetically_equivalent, nf.embedding, nf.galois_group, nf.maximal_cm_subfield, nf.minimal_sibling, nf.reflex_field, nf.root_discriminant, nf.separable, nf.serre_odlyzko_bound, nf.signature nf.degree_mathlib_def: nf.degree nf.discriminant: cmf.self_twist, ec.analytic_sha_order, ec.bsdconjecture, nf.abs_discriminant, nf.arithmetically_equivalent, nf.class_number_formula, nf.minimal_sibling, nf.poly_discriminant, nf.radical_discriminant, nf.root_discriminant, nf.unramified_prime nf.embedding: cmf.embedding, cmf.q-expansion, ec.period, nf.reflex_field nf.fundamental_units: nf.rank, nf.regulator nf.galois_closure: nf.galois_group, nf.galois_root_discriminant, nf.sibling, nf.stem_field nf.galois_group: artin, character.dirichlet.galois_orbit, nf.abelian, nf.arithmetically_equivalent, nf.minimal_sibling nf.ideal_class_group: ec.global_minimal_model, ec.obstruction_class, nf.class_number, nf.narrow_class_number nf.integral: ec.local_minimal_model, ec.potential_good_reduction, ec.reduction nf.integral_basis: nf.discriminant nf.is_galois: artin.conductor, ec.isogeny, lf.automorphism_group, lf.inertia_group, lf.wild_inertia_group, nf.stem_field nf.local_algebra: nf.padic_completion nf.minimal_polynomial: nf.complex_embedding, nf.embedding, nf.generator nf.narrow_class_group: nf.narrow_class_number nf.order: ag.complex_multiplication, ec.complex_multiplication, ec.q.minimal_twist, nf.monomial_order, nf.zk_index nf.place: ec.analytic_sha_order, ec.period nf.polredabs: nf.ideal_labels nf.poly_discriminant: nf.polredabs nf.prime: artin.conductor, ec.analytic_sha_order, ec.bad_reduction, ec.bsdconjecture, ec.good_reduction, ec.minimal_discriminant, ec.q.serre_invariants, nf.padic_completion nf.ramified_primes: artin.ramified_primes, nf.max_p nf.real_embedding: nf.embedding, nf.place, nf.signature, nf.unit_signature_rank nf.reflex_field: nf.reflex_reflex_field nf.regulator: nf.class_number_formula nf.ring_of_integers: cmf.coefficient_ring, ec.conductor, ec.integral_model, ec.minimal_discriminant, ec.reduction_type, nf.ideal_class_group, nf.integral_basis, nf.monogenic, nf.monomial_order, nf.place, nf.poly_discriminant, nf.prime, nf.unit_group, nf.zk_index, ring.dedekind_domain nf.root_discriminant: nf.galois_root_discriminant, nf.serre_odlyzko_bound nf.separable: nf.galois_closure, nf.galois_group, nf.separable_algebra, nf.sibling nf.separable_algebra: nf.local_algebra nf.sibling: cmf.artin_field, cmf.projective_field, nf.arithmetically_equivalent, nf.minimal_sibling nf.signature: nf.arithmetically_equivalent, nf.class_number_formula, nf.embedding nf.totally_imaginary: nf.cm_field, nf.narrow_class_number nf.totally_positive: nf.narrow_class_group nf.totally_real: cmf.selfdual, nf.cm_field, nf.relative_class_number, st_group.definition nf.unit_group: nf.fundamental_units, nf.torsion nf.weil_height: ec.canonical_height, ec.q.canonical_height nf.zk_index: nf.inessential_prime ring: ec.ring, ring.characteristic, ring.field, ring.field_of_fractions_mathlib, ring.ideal, ring.integral, ring.integral_domain, ring.irreducible, ring.maximal_ideal, ring.noetherian, ring.prime_ideal, ring.unit, ring.zero_divisor ring.a-field: modcurve.xn ring.characteristic: ec.complex_multiplication, ec.simple_equation, ec.twists, lf.local_field, lf.padic_field ring.dedekind_domain: nf.padic_completion ring.field: ag.affine_space, ag.base_change, ag.minimal_field, ag.projective_space, ag.variety, ec.discriminant, ec.simple_equation, ec.twists, group.galois.absolute, lf.automorphism_group, lf.local_field, nf.galois_group, ring.a-field, ring.characteristic, ring.dedekind_domain, ring.field_of_fractions ring.field_of_fractions: nf.padic_completion, ring.fractional_ideal, ring.integrally_closed, ring.principal_fractional_ideal ring.field_of_fractions_mathlib: ring.field_of_fractions ring.fractional_ideal: nf.ideal_class_group, nf.padic_completion, ring.dedekind_domain ring.ideal: ec.invariants, ring.dedekind_domain, ring.maximal_ideal, ring.noetherian, ring.prime_ideal ring.integral: nf.integral, nf.ring_of_integers, ring.integrally_closed ring.integral_domain: nf.padic_completion, ring.dedekind_domain, ring.field_of_fractions, ring.fractional_ideal, ring.integrally_closed, ring.principal_fractional_ideal ring.integrally_closed: ring.dedekind_domain ring.irreducible: nf.padic_completion ring.maximal_ideal: lf.maximal_ideal, ring.dedekind_domain ring.noetherian: ring.dedekind_domain ring.prime_ideal: ag.variety, nf.place, nf.prime, ring.dedekind_domain ring.principal_fractional_ideal: nf.ideal_class_group ring.unit: lf.maximal_ideal, ring.irreducible ring.zero_divisor: ring.integral_domain specialfunction.gamma: lfunction.functional_equation st_group.definition: ec.invariants st_group.symplectic_form: st_group.usp st_group.usp: st_group.definition b:A where b references all a in B af.divisor_function: af, af.multiplicative ag.abelian_variety: ag.variety, ec ag.affine_space: ring.field ag.base_change: ag.variety, ring.field ag.base_field: ag.abelian_variety, ag.minimal_field ag.complex_multiplication: ag.abelian_variety, ag.dimension, ag.endomorphism_algebra, ag.endomorphism_ring, ag.geom_simple, nf.cm_field, nf.degree, nf.order ag.curve: ag.variety ag.curve.genus: ag.riemann_surface ag.curve.smooth: ag.curve, ag.singular_point ag.dimension: ag.irreducible, ag.variety ag.endomorphism_algebra: ag.abelian_variety, ag.endomorphism_ring ag.endomorphism_ring: ag.abelian_variety ag.geom_endomorphism_ring: ag.endomorphism_ring ag.geom_simple: ag.abelian_variety, ag.simple ag.hyperelliptic_curve: ag.curve, ag.curve.genus ag.irreducible: ag.variety ag.jacobian: ag.abelian_variety ag.minimal_field: ag.base_change, ag.curve.genus, ag.variety, ring.field ag.mordell_weil: ag.abelian_variety, ag.dimension ag.projective_space: ring.field ag.quotient_curve: ag.curve, ag.variety, g2c.aut_grp ag.simple: ag.abelian_variety ag.variety: ag.affine_space, ag.projective_space, ring.field, ring.prime_ideal alg.binary_operation.associative: alg.binary_operation alg.binary_operation.commutative: alg.binary_operation alg.binary_operation.identity: alg.binary_operation alg.binary_operation.inverse: alg.binary_operation, alg.binary_operation.identity artin: group.galois.absolute, nf.galois_group artin.conductor: artin, artin.unramified_primes, gg.galois_group, lf.inertia_group, lf.padic_field, lf.wild_inertia_group, nf.is_galois, nf.prime artin.number_field: artin, nf artin.parity: artin artin.ramified_primes: artin, artin.number_field, nf.ramified_primes artin.unramified_primes: artin, artin.number_field, artin.ramified_primes av.isogeny: ag.abelian_variety av.simple: ag.abelian_variety av.tate_module: av.isogeny, group.galois.absolute av.twist: ag.abelian_variety, ag.base_change character.dirichlet.conductor: character.dirichlet character.dirichlet.galois_orbit: character.dirichlet, character.dirichlet.modulus, character.dirichlet.order, character.dirichlet.value_field, nf.galois_group character.dirichlet.galois_orbit_index: character.dirichlet, character.dirichlet.galois_orbit, character.dirichlet.modulus, character.dirichlet.order, character.dirichlet.principal, character.dirichlet.value_field character.dirichlet.galois_orbit_label: character.dirichlet, character.dirichlet.galois_orbit, character.dirichlet.galois_orbit_index character.dirichlet.induce: character.dirichlet, character.dirichlet.modulus character.dirichlet.minimal: character.dirichlet, character.dirichlet.conductor, character.dirichlet.modulus, character.dirichlet.order, character.dirichlet.primitive, character.dirichlet.principal character.dirichlet.order: character.dirichlet, character.dirichlet.modulus, character.dirichlet.principal character.dirichlet.primitive: character.dirichlet, character.dirichlet.conductor, character.dirichlet.induce, character.dirichlet.modulus character.dirichlet.principal: character.dirichlet, character.dirichlet.induce, character.dirichlet.modulus character.dirichlet.value_field: character.dirichlet.order cmf: character.dirichlet, cmf.space_mathlib_def, group.fuchsian.cusps, group.sl2z, mf.upper_half_plane cmf.analytic_conductor: cmf.newform cmf.analytic_rank: cmf.coefficient_field, cmf.cusp_form, cmf.q-expansion, cmf.selfdual, lfunction.analytic_rank cmf.artin_field: cmf.galois_representation, cmf.newform, cmf.weight, nf.sibling cmf.artin_image: cmf.artin_field, cmf.galois_representation, cmf.newform, cmf.weight cmf.atkin-lehner: cmf.cusp_form, cmf.hecke_operator, cmf.weight cmf.bad_prime: cmf, cmf.level cmf.character: character.dirichlet, cmf cmf.cm_form: cmf, cmf.self_twist cmf.coefficient_field: cmf.cusp_form, cmf.fouriercoefficients, cmf.hecke_operator cmf.coefficient_ring: cmf, cmf.coefficient_field, cmf.hecke_operator, cmf.newform, nf.ring_of_integers cmf.cusp_form: character.dirichlet, cmf, cmf.cusp_form_mathlib_def, cmf.fouriercoefficients, cmf.weight, group.fuchsian.cusps, group.sl2z cmf.cusp_form_subspace_mathlib_def: cmf.cusp_form, cmf.space_mathlib_def cmf.decomposition.new.gamma0chi: cmf.hecke_operator, cmf.newform cmf.defining_polynomial: cmf.coefficient_field, nf cmf.dimension: cmf.dimension_mathlib_def, cmf.galois_orbit, cmf.newform, cmf.newform_subspace cmf.dimension_mathlib_def: cmf.space, cmf.space_mathlib_def cmf.distinguishing_primes: cmf.galois_orbit, cmf.hecke_operator, cmf.newform, cmf.newspace cmf.dualform: cmf.coefficient_field, cmf.cusp_form, cmf.newform, cmf.q-expansion, cmf.selfdual, lfunction.dual, nf.cm_field cmf.eisenstein: af.bernoulli_numbers, af.divisor_function, cmf, cmf.level, cmf.q-expansion, cmf.weight, group.sl2z cmf.eisenstein_form: character.dirichlet, cmf, cmf.cusp_form, cmf.eisenstein_series, cmf.petersson_scalar_product, cmf.weight, group.sl2z cmf.eisenstein_label: character.dirichlet, character.dirichlet.galois_orbit, character.dirichlet.galois_orbit_label, cmf.coefficient_field, cmf.eisenstein_newform, cmf.embedding, cmf.galois_orbit, cmf.level, cmf.relative_dimension, cmf.weight cmf.eisenstein_newform: cmf.eisenstein_newspace, cmf.fouriercoefficients, cmf.hecke_operator cmf.eisenstein_newspace: character.dirichlet, character.dirichlet.induce, character.dirichlet.modulus, cmf, cmf.character, cmf.eisenstein_form, cmf.eisenstein_series, cmf.level, cmf.weight cmf.eisenstein_series: character.dirichlet, character.dirichlet.primitive, cmf.weight cmf.embedding: character.dirichlet, character.dirichlet.value_field, cmf.character, cmf.coefficient_field, cmf.galois_orbit, cmf.q-expansion, lfunction, nf.embedding cmf.embedding_label: character.dirichlet.galois_orbit_label, cmf.cusp_form, cmf.embedding, cmf.level, cmf.weight cmf.eta_quotient: mf.half_integral_weight.dedekind_eta cmf.fouriercoefficients: cmf, group.fuchsian.cusps, group.fuchsian.cusps.width cmf.fouriercoefficients_mathlib_def: cmf, cmf.q-expansion cmf.fricke: cmf.analytic_rank, cmf.atkin-lehner, lfunction, lfunction.functional_equation cmf.galois_conjugate: cmf.newform, nf.degree cmf.galois_orbit: cmf.galois_conjugate, cmf.newform, cmf.newform_subspace cmf.galois_representation: artin, artin.conductor, artin.parity, cmf.newform, cmf.weight cmf.hecke_operator: character.dirichlet, cmf, cmf.cusp_form, cmf.level, cmf.petersson_scalar_product, cmf.weight cmf.hecke_orbit: cmf.cusp_form, cmf.hecke_operator, cmf.level cmf.hecke_ring_generators: cmf.coefficient_ring, cmf.newform, cmf.q-expansion cmf.heckecharpolys: cmf.hecke_operator, cmf.newform, cmf.newform_subspace cmf.inner_twist: character.dirichlet, character.dirichlet.galois_orbit, character.dirichlet.primitive, cmf.cm_form, cmf.coefficient_field, cmf.galois_conjugate, cmf.galois_orbit, cmf.newform, cmf.rm_form, cmf.self_twist cmf.inner_twist_count: character.dirichlet, cmf.coefficient_field, cmf.dimension, cmf.inner_twist, cmf.newform, cmf.self_twist, cmf.weight cmf.inner_twist_multiplicity: character.dirichlet, character.dirichlet.galois_orbit, cmf.embedding, cmf.inner_twist, cmf.newform cmf.label: character.dirichlet, character.dirichlet.galois_orbit, character.dirichlet.galois_orbit_label, cmf.coefficient_field, cmf.embedding, cmf.galois_orbit, cmf.level, cmf.newform, cmf.relative_dimension, cmf.weight cmf.labels: character.dirichlet, character.dirichlet.galois_orbit, character.dirichlet.galois_orbit_label, cmf.coefficient_field, cmf.embedding, cmf.galois_orbit, cmf.level, cmf.relative_dimension, cmf.weight cmf.level: cmf, group.sl2z cmf.maximal: cmf.character, cmf.dimension, cmf.galois_orbit, cmf.newform cmf.minimal_twist: character.dirichlet.minimal, cmf.character, cmf.label, cmf.level, cmf.newform, cmf.twist, cmf.twist_minimal cmf.minus_space: cmf.fricke cmf.newform: cmf.fouriercoefficients, cmf.hecke_operator, cmf.newspace cmf.newform_subspace: cmf.newform, cmf.newspace cmf.newspace: character.dirichlet, character.dirichlet.induce, character.dirichlet.modulus, cmf, cmf.character, cmf.cusp_form, cmf.level, cmf.petersson_scalar_product, cmf.weight cmf.nontrivial_twist: cmf.inner_twist, cmf.self_twist cmf.oldspace: character.dirichlet.conductor, character.dirichlet.induce, character.dirichlet.primitive, cmf, cmf.character, cmf.cusp_form, cmf.level, cmf.newspace, cmf.weight cmf.petersson_scalar_product: cmf.cusp_form, cmf.petersson_scalar_product_mathlib_def, group.fuchsian.fundamental_domain, group.subgroup.index cmf.plus_space: cmf.fricke cmf.projective_field: cmf.galois_representation, cmf.newform, cmf.weight, nf, nf.sibling cmf.projective_image: cmf.galois_representation, cmf.newform, cmf.weight cmf.q-expansion: cmf.cusp_form, cmf.fouriercoefficients, cmf.galois_orbit, cmf.newform, cmf.q-expansion_mathlib_def, group.fuchsian.cusps, nf, nf.embedding cmf.q-expansion_mathlib_def: cmf cmf.relative_dimension: cmf.newform cmf.rm_form: cmf, cmf.self_twist cmf.satake_angles: cmf.satake_parameters cmf.satake_parameters: cmf.bad_prime, cmf.character, cmf.hecke_operator, cmf.level, cmf.newform, cmf.weight cmf.sato_tate: cmf.cm_form, cmf.newform, cmf.weight cmf.self_twist: character.dirichlet, character.dirichlet.order, character.dirichlet.primitive, cmf.level, cmf.newform, cmf.projective_image, cmf.weight, nf.discriminant cmf.selfdual: cmf.coefficient_field, cmf.cusp_form, cmf.newform, cmf.q-expansion, lfunction.self-dual, nf.cm_field, nf.totally_real cmf.shimura_correspondence: character.dirichlet cmf.space: cmf, cmf.character, cmf.cusp_form, cmf.level, cmf.space_mathlib_def, cmf.weight cmf.space_trace_form: cmf.newform, cmf.newspace cmf.stark_unit: cmf.artin_field, cmf.galois_representation, cmf.newform, cmf.weight cmf.sturm_bound: cmf.character, cmf.fouriercoefficients, cmf.level, cmf.newform, cmf.weight cmf.sturm_bound_gamma1: cmf.fouriercoefficients, cmf.level, cmf.newform, cmf.weight cmf.subspaces: character.dirichlet, character.dirichlet.conductor, character.dirichlet.induce, character.dirichlet.modulus, cmf, cmf.character, cmf.cusp_form, cmf.cusp_form_subspace_mathlib_def, cmf.level, cmf.petersson_scalar_product, cmf.space, cmf.weight cmf.trace_bound: cmf.coefficient_field, cmf.dimension, cmf.galois_orbit, cmf.newform, cmf.newspace, cmf.q-expansion cmf.trace_form: cmf.coefficient_field, cmf.dimension, cmf.newform, cmf.newspace cmf.twist: character.dirichlet, character.dirichlet.conductor, character.dirichlet.galois_orbit, character.dirichlet.primitive, cmf.galois_conjugate, cmf.galois_orbit, cmf.inner_twist, cmf.newform cmf.twist_minimal: character.dirichlet.minimal, cmf.character, cmf.galois_orbit, cmf.label, cmf.level, cmf.newform, cmf.twist cmf.twist_multiplicity: character.dirichlet.galois_orbit, character.dirichlet.primitive, cmf.galois_orbit, cmf.inner_twist, cmf.inner_twist_count, cmf.twist cmf.weight: cmf ec: ag.curve, ag.curve.genus, ag.curve.smooth ec.additive_reduction: ec, nf ec.analytic_sha_order: ec, ec.base_change, ec.mordell_weil_group, ec.period, ec.rank, ec.regulator, ec.tamagawa_number, ec.torsion_subgroup, group.abelian, group.galois.absolute, group.order, group.torsion, nf, nf.discriminant, nf.place, nf.prime ec.bad_reduction: ec, ec.additive_reduction, ec.discriminant, ec.nonsplit_multiplicative_reduction, ec.split_multiplicative_reduction, nf, nf.prime ec.base_change: ec.j_invariant ec.bsdconjecture: ag.abelian_variety, ec, ec.analytic_sha_order, ec.period, ec.rank, ec.regulator, ec.tamagawa_number, ec.torsion_subgroup, lfunction, lfunction.analytic_rank, lfunction.central_point, lfunction.leading_coeff, nf, nf.discriminant, nf.prime ec.canonical_height: ec, ec.mordell_weil_group, nf, nf.weil_height ec.complex_multiplication: ag.complex_multiplication, ec, ec.endomorphism_ring, ec.geom_endomorphism_ring, ec.j_invariant, nf.class_number, nf.order, ring.characteristic ec.conductor: ec, ec.additive_reduction, ec.bad_reduction, ec.good_reduction, ec.multiplicative_reduction, nf, nf.ring_of_integers ec.discriminant: ag.curve.smooth, ec, ec.weierstrass_coeffs, ring.field ec.endomorphism: ag.abelian_variety, ag.endomorphism_ring, ec ec.endomorphism_ring: ag.abelian_variety, ag.endomorphism_ring, ec, ec.endomorphism ec.galois_rep: ec, ec.complex_multiplication, ec.padic_tate_module, gl2.index, gl2.level, gl2.open, group.galois.absolute, nf ec.galois_rep_adelic_image: ec.complex_multiplication, ec.galois_rep, gl2.open, modcurve ec.galois_rep_modell_image: ec, ec.galois_rep, gl2.borel, gl2.exceptional, gl2.nonsplit_cartan, gl2.normalizer_nonsplit_cartan, gl2.normalizer_split_cartan, gl2.split_cartan, nf ec.geom_endomorphism_ring: ag.abelian_variety, ag.geom_endomorphism_ring, ec.endomorphism_ring ec.global_minimal_model: ec, ec.integral_model, ec.local_minimal_model, ec.weierstrass_coeffs, nf, nf.class_number, nf.ideal_class_group ec.good_ordinary_reduction: ec, nf ec.good_reduction: ag.curve.smooth, ec, nf, nf.prime ec.good_supersingular_reduction: ec, nf ec.integral_model: ec, ec.weierstrass_coeffs, nf.ring_of_integers ec.invariants: ec, ec.conductor, ec.discriminant, ec.endomorphism_ring, ec.j_invariant, ec.minimal_discriminant, ec.weierstrass_coeffs, nf, ring.ideal, st_group.definition ec.isogeny: ag.base_field, av.isogeny, ec, ec.endomorphism, ec.endomorphism_ring, group.homomorphism, nf, nf.is_galois ec.isogeny_class: ec, ec.isogeny ec.isogeny_class_degree: ec, ec.isogeny, ec.isogeny_class ec.isogeny_graph: ec, ec.isogeny_class ec.isogeny_matrix: ec, ec.isogeny_class ec.isomorphism: ec, ec.isogeny ec.j_invariant: ec, ec.discriminant, ec.isomorphism, ec.weierstrass_coeffs ec.kodaira_symbol: ec, ec.local_minimal_model, ec.reduction_type, nf ec.local_data: ec, ec.kodaira_symbol, ec.reduction_type, ec.tamagawa_number, nf ec.local_minimal_discriminant: ec, ec.local_minimal_model, nf ec.local_minimal_model: ec, ec.discriminant, ec.weierstrass_coeffs, nf, nf.integral ec.maximal_elladic_galois_rep: ec, ec.complex_multiplication, ec.galois_rep, ec.geom_endomorphism_ring, nf ec.maximal_galois_rep: ec, ec.complex_multiplication, ec.galois_rep, ec.geom_endomorphism_ring, gl2.borel, gl2.normalizer_nonsplit_cartan, gl2.normalizer_split_cartan, nf ec.minimal_discriminant: ec, ec.discriminant, ec.global_minimal_model, ec.local_minimal_discriminant, ec.weierstrass_coeffs, nf, nf.prime, nf.ring_of_integers ec.mordell_weil_group: ag.abelian_variety, ag.mordell_weil, ec, nf ec.mordell_weil_theorem: ec, ec.mordell_weil_group, nf ec.multiplicative_reduction: ec, ec.nonsplit_multiplicative_reduction, ec.split_multiplicative_reduction, nf ec.mw_generators: ec, ec.mordell_weil_group, ec.rank, ec.torsion_subgroup, group.abelian, nf ec.nonsplit_multiplicative_reduction: ec, nf ec.obstruction_class: ec, ec.global_minimal_model, nf, nf.ideal_class_group ec.padic_tate_module: av.tate_module, ec.endomorphism, group.galois.absolute ec.period: ec, ec.base_change, ec.discriminant, ec.global_minimal_model, ec.minimal_discriminant, ec.q.period_lattice, ec.weierstrass_coeffs, nf, nf.embedding, nf.place ec.potential_good_reduction: ec, ec.good_reduction, ec.j_invariant, nf, nf.integral ec.q: ec.q.discriminant, ec.q.minimal_weierstrass_equation ec.q.abc_quality: ec, ec.j_invariant, ec.q.conductor ec.q.analytic_rank: ag.mordell_weil, ec, ec.mordell_weil_group, lfunction, lfunction.central_point, lfunction.functional_equation, lfunction.sign ec.q.analytic_sha_order: ec, group.order ec.q.bsdconjecture: ag.abelian_variety, ec, ec.analytic_sha_order, ec.mordell_weil_theorem, ec.q.real_period, ec.rank, ec.regulator, ec.tamagawa_number, ec.torsion_order, lfunction, lfunction.central_point ec.q.canonical_height: ec, ec.regulator, nf.weil_height ec.q.conductor: ec, ec.additive_reduction, ec.multiplicative_reduction ec.q.cremona_label: ec, ec.isogeny, ec.isogeny_class, ec.isomorphism, ec.q.conductor, ec.q.optimal ec.q.discriminant: ec, ec.discriminant, ec.q.minimal_weierstrass_equation ec.q.endomorphism_ring: ag.abelian_variety, ag.endomorphism_ring, ec, ec.endomorphism, ec.geom_endomorphism_ring ec.q.faltings_height: ec, ec.discriminant, ec.j_invariant, ec.q.period_lattice, ec.semistable ec.q.faltings_ratio: ec, ec.isogeny, ec.q.faltings_height, ec.q.period_lattice, group.subgroup.index ec.q.j_invariant: ec, ec.q.discriminant, ec.weierstrass_coeffs ec.q.kodaira_symbol: ec.q.minimal_weierstrass_equation, ec.q.reduction_type ec.q.lmfdb_label: ec, ec.conductor, ec.isogeny_class, ec.isomorphism, ec.q.conductor, ec.q.minimal_weierstrass_equation ec.q.manin_constant: ec, ec.isogeny, ec.q.conductor, ec.q.modular_parametrization, ec.q.optimal, ec.semistable ec.q.minimal_twist: ec, ec.complex_multiplication, ec.isogeny_class, ec.j_invariant, ec.minimal_discriminant, ec.q.conductor, ec.twists, nf.order ec.q.modular_degree: ec, ec.q.modular_parametrization ec.q.modular_parametrization: ec ec.q.naive_height: ec, ec.weierstrass_coeffs ec.q.optimal: ec.isogeny_class, ec.q, ec.q.conductor ec.q.period_lattice: ec, ec.global_minimal_model, ec.q.discriminant, ec.q.real_period, ec.weierstrass_coeffs, group.rank ec.q.real_period: ec.q.minimal_weierstrass_equation, ec.weierstrass_coeffs, ec.weierstrass_isomorphism ec.q.reduction_type: ec.q.minimal_weierstrass_equation ec.q.regulator: ec, ec.canonical_height, ec.mordell_weil_group, nf ec.q.semistable: ec, ec.bad_reduction, ec.reduction_type ec.q.serre_invariants: cmf.level, cmf.weight, ec.galois_rep, nf.prime ec.q.special_value: ec, ec.q.bsdconjecture, lfunction.normalization ec.q.szpiro_ratio: ec, ec.minimal_discriminant, ec.q.conductor, ec.q.j_invariant ec.q.torsion_growth: ec, ec.torsion_subgroup, nf, nf.degree ec.q_curve: ec, ec.base_change, ec.complex_multiplication, ec.isogeny, nf ec.rank: ec, ec.isogeny, ec.isogeny_class, ec.mordell_weil_group, ec.mordell_weil_theorem, ec.torsion_subgroup, nf ec.reduction: ec, ec.bad_reduction, ec.j_invariant, ec.potential_good_reduction, ec.reduction_type, ec.semistable, nf.integral ec.reduction_type: ec, ec.bad_reduction, ec.good_reduction, nf, nf.ring_of_integers ec.regulator: ec, ec.base_change, ec.canonical_height, ec.mordell_weil_group, ec.rank, nf, nf.degree ec.ring: ec, ec.good_reduction, ec.scheme, ring ec.semi_global_minimal_model: ec, ec.discriminant, ec.local_minimal_model, ec.minimal_discriminant, nf, nf.class_number ec.semistable: ec, ec.bad_reduction, ec.reduction_type ec.simple_equation: ec, ec.bad_reduction, ec.good_reduction, ec.q.minimal_weierstrass_equation, ring.characteristic, ring.field ec.special_value: ec, ec.bsdconjecture, lfunction, lfunction.leading_coeff, lfunction.normalization, nf ec.split_multiplicative_reduction: ec, nf ec.tamagawa_number: ec, ec.good_reduction, nf ec.torsion_order: ec, ec.mordell_weil_group, ec.mordell_weil_theorem, ec.torsion_subgroup ec.torsion_subgroup: ec.mordell_weil_group, ec.mordell_weil_theorem ec.twists: av.twist, ec, ec.j_invariant, g2c.aut_grp, ring.characteristic, ring.field ec.weierstrass_coeffs: ec ec.weierstrass_isomorphism: ec.isomorphism, ec.weierstrass_coeffs g2c.aut_grp: ag.curve, g2c.g2curve g2c.g2curve: ag.hyperelliptic_curve, g2c.discriminant, g2c.minimal_equation g2c.good_reduction: ag.jacobian, ag.variety g2c.minimal_equation: ag.curve.genus, ag.curve.smooth, ag.hyperelliptic_curve, g2c.discriminant, g2c.good_reduction gl2.exceptional: gl2.borel, gl2.normalizer_cartan gl2.index: gl2.level, gl2.open, gl2.profinite gl2.level: gl2.open gl2.nonsplit_cartan: gl2.cartan gl2.normalizer_cartan: gl2.cartan gl2.normalizer_nonsplit_cartan: gl2.nonsplit_cartan gl2.normalizer_split_cartan: gl2.split_cartan gl2.open: gl2.profinite gl2.split_cartan: gl2.cartan group: alg.binary_operation, alg.binary_operation.associative, alg.binary_operation.identity, alg.binary_operation.inverse group.abelian: alg.binary_operation, alg.binary_operation.commutative, group group.automorphism: group, group.isomorphism group.characteristic_subgroup: group, group.automorphism, group.subgroup group.coset: group, group.subgroup group.frattini_subgroup: group.characteristic_subgroup, group.maximal_subgroup, group.subgroup.normal group.fuchsian.cusps: group.sl2z group.fuchsian.cusps.width: group.fuchsian.cusps, group.sl2z group.fuchsian.fundamental_domain: group.sl2z group.galois.absolute: ring.field group.generators: group, group.automorphism group.haar_measure: group, group.order group.homomorphism: group group.isomorphism: group.homomorphism group.normal_series: group, group.subgroup, group.subgroup.normal group.order: group group.presentation: group.normal_series group.rank: group, group.frattini_subgroup, group.generators, group.presentation group.subgroup: alg.binary_operation, alg.binary_operation.identity, alg.binary_operation.inverse, group group.subgroup.index: group.coset group.subgroup.normal: alg.binary_operation, group, group.coset, group.subgroup group.sylow_subgroup: group, group.order, group.subgroup group.torsion: group, group.abelian lf.automorphism_group: nf.is_galois, ring.field lf.inertia_group: lf.maximal_ideal, lf.padic_field, lf.residue_field, nf.is_galois lf.local_field: nf.absolute_value, ring.characteristic, ring.field lf.maximal_ideal: lf.local_field, lf.ring_of_integers, nf.absolute_value, ring.maximal_ideal, ring.unit lf.padic_field: lf.local_field, lf.qp, ring.characteristic lf.residue_field: lf.maximal_ideal, lf.ring_of_integers lf.ring_of_integers: lf.local_field, nf.absolute_value lf.wild_inertia_group: group.sylow_subgroup, lf.inertia_group, nf.is_galois lfunction: lfunction.dirichlet_series, lfunction.euler_product, lfunction.functional_equation lfunction.analytic_rank: lfunction, lfunction.central_point lfunction.arithmetic: lfunction lfunction.central_point: lfunction, lfunction.critical_line, lfunction.functional_equation lfunction.critical_line: lfunction, lfunction.functional_equation lfunction.dual: lfunction lfunction.functional_equation: lfunction.gamma_factor, specialfunction.gamma lfunction.gamma_factor: lfunction.euler_product lfunction.leading_coeff: lfunction.arithmetic, lfunction.central_point lfunction.normalization: lfunction.functional_equation lfunction.rh: lfunction lfunction.sign: lfunction.functional_equation mf.upper_half_plane: group.sl2z modcurve: ag.curve.smooth, ag.quotient_curve, cmf.congruence_subgroup, ec, ec.galois_rep, gl2.level, gl2.open, mf.upper_half_plane, modcurve.cusps, modcurve.level_structure, modcurve.xn modcurve.level_structure: ec, ec.base_change, ec.galois_rep, gl2.level, gl2.open, nf modcurve.xn: alg.symplectic_isomorphism, cmf.congruence_subgroup, ec.ring, gl2.open, mf.upper_half_plane, ring.a-field nf: nf.degree nf.abelian: nf, nf.galois_group nf.abs_discriminant: nf, nf.discriminant nf.arithmetically_equivalent: nf, nf.degree, nf.discriminant, nf.galois_group, nf.sibling, nf.signature nf.class_number: nf, nf.ideal_class_group nf.class_number_formula: nf, nf.class_number, nf.discriminant, nf.regulator, nf.signature nf.cm_field: nf, nf.totally_imaginary, nf.totally_real nf.complex_embedding: nf, nf.minimal_polynomial nf.conductor: nf, nf.abelian nf.defining_polynomial: nf nf.degree: nf.degree_mathlib_def nf.dirichlet_group: character.dirichlet, nf.abelian, nf.conductor nf.discriminant: nf, nf.integral_basis nf.embedding: nf, nf.complex_embedding, nf.degree, nf.minimal_polynomial, nf.real_embedding, nf.signature nf.fundamental_units: nf, nf.unit_group nf.galois_closure: nf.separable nf.galois_group: lf.automorphism_group, nf.degree, nf.galois_closure, nf.separable, ring.field nf.galois_root_discriminant: nf, nf.galois_closure, nf.root_discriminant nf.generator: nf, nf.defining_polynomial, nf.minimal_polynomial nf.ideal_class_group: nf, nf.ring_of_integers, ring.fractional_ideal, ring.principal_fractional_ideal nf.ideal_labels: nf.polredabs nf.inessential_prime: nf, nf.zk_index nf.integral: nf, ring.integral nf.integral_basis: nf, nf.ring_of_integers nf.local_algebra: nf, nf.separable_algebra nf.max_p: nf, nf.ramified_primes nf.maximal_cm_subfield: nf, nf.cm_field, nf.degree nf.minimal_polynomial: nf nf.minimal_sibling: nf, nf.degree, nf.discriminant, nf.galois_group, nf.sibling nf.monogenic: nf, nf.ring_of_integers nf.monomial_order: nf, nf.order, nf.ring_of_integers nf.narrow_class_group: nf, nf.totally_positive nf.narrow_class_number: nf, nf.class_number, nf.ideal_class_group, nf.narrow_class_group, nf.totally_imaginary nf.order: nf nf.padic_completion: lf.ring_of_integers, nf, nf.local_algebra, nf.prime, ring.dedekind_domain, ring.field_of_fractions, ring.fractional_ideal, ring.integral_domain, ring.irreducible nf.place: nf, nf.absolute_value, nf.complex_embedding, nf.real_embedding, nf.ring_of_integers, ring.prime_ideal nf.polredabs: nf, nf.poly_discriminant nf.poly_discriminant: nf, nf.discriminant, nf.ring_of_integers nf.prime: nf, nf.ring_of_integers, ring.prime_ideal nf.radical_discriminant: nf, nf.discriminant nf.rank: nf, nf.fundamental_units nf.reflex_field: group.subgroup, nf.cm_field, nf.complex_embedding, nf.degree, nf.embedding nf.reflex_reflex_field: nf.cm_field, nf.reflex_field nf.regulator: nf, nf.fundamental_units nf.relative_class_number: nf, nf.class_number, nf.cm_field, nf.totally_real nf.ring_of_integers: nf, ring.integral nf.root_discriminant: nf, nf.degree, nf.discriminant nf.separable: nf.degree nf.separable_algebra: nf.separable nf.serre_odlyzko_bound: lfunction.rh, nf, nf.degree, nf.root_discriminant nf.sibling: nf.galois_closure, nf.separable nf.signature: nf, nf.complex_embedding, nf.degree, nf.real_embedding nf.stem_field: nf.galois_closure, nf.is_galois nf.torsion: nf, nf.unit_group nf.totally_imaginary: nf nf.totally_positive: nf nf.totally_real: nf nf.unit_group: nf, nf.ring_of_integers nf.unit_signature_rank: nf, nf.real_embedding nf.unramified_prime: nf, nf.discriminant nf.weil_height: ag.variety, nf nf.weil_polynomial: ag.abelian_variety, av.simple nf.zk_index: nf, nf.order, nf.ring_of_integers ring: alg.binary_operation, alg.binary_operation.associative, alg.binary_operation.commutative, alg.binary_operation.identity, group.abelian ring.a-field: ring.field ring.characteristic: group, ring, ring.field ring.dedekind_domain: nf, nf.ring_of_integers, ring.field, ring.fractional_ideal, ring.ideal, ring.integral_domain, ring.integrally_closed, ring.maximal_ideal, ring.noetherian, ring.prime_ideal ring.field: alg.binary_operation.inverse, ring ring.field_of_fractions: ring.field, ring.field_of_fractions_mathlib, ring.integral_domain ring.field_of_fractions_mathlib: ring ring.fractional_ideal: ring.field_of_fractions, ring.integral_domain ring.ideal: group.subgroup, ring ring.integral: ring ring.integral_domain: ring, ring.zero_divisor ring.integrally_closed: ring.field_of_fractions, ring.integral, ring.integral_domain ring.irreducible: ring, ring.unit ring.maximal_ideal: ring, ring.ideal ring.noetherian: ring, ring.ideal ring.prime_ideal: ring, ring.ideal ring.principal_fractional_ideal: ring.field_of_fractions, ring.integral_domain ring.unit: group, ring ring.zero_divisor: ring st_group.definition: ag.abelian_variety, ag.dimension, artin, ec, group.haar_measure, nf.cm_field, nf.totally_real, st_group.usp st_group.usp: st_group.symplectic_form