A number field is a finite degree field extension of the field $\Q$ of rational numbers. In LMFDB, number fields are identified by a label.
Knowl status:
- Review status: reviewed
- Last edited by Alina Bucur on 2018-07-07 19:29:57
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- ag.canonical_height
- ag.good_reduction
- ag.potential_good_reduction
- ag.regulator
- ag.selmer_group
- ag.tate_shafarevich
- artin.number_field
- av.potential_toric_rank
- character.hecke
- cmf.defining_polynomial
- cmf.projective_field
- cmf.q-expansion
- dq.ecnf.extent
- dq.ecnf.reliability
- ec.additive_reduction
- ec.analytic_sha_order
- ec.bad_reduction
- ec.bsdconjecture
- ec.canonical_height
- ec.conductor
- ec.conductor_label
- ec.galois_rep
- ec.galois_rep_elladic_image
- 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.local_root_number
- 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.split_multiplicative_reduction
- ec.tamagawa_number
- g2c.hasse_weil_conjecture
- g2c.known_rational_points
- g2c.locally_solvable
- g2c.mw_generator
- g2c.num_rat_pts
- g2c.torsion
- g2c.torsion_order
- gg.arithmetically_equiv_input
- gg.arithmetically_equivalent
- lfunction.coefficient_field
- lfunction.root_analytic_conductor
- lfunction.underlying_object
- mf.base_change
- mf.bianchi
- mf.cm
- mf.gl2.history.hecke
- mf.gl2.history.varieties
- mf.hilbert
- mf.hilbert.level_norm
- mf.siegel.defining_polynomial
- modcurve.level_structure
- modlgal
- nf.14.2.20325604337285010030592.1.bottom
- nf.3.1.503.1.bottom
- nf.4.0.225.1.top
- nf.abelian
- nf.abs_discriminant
- nf.algebraic_closure
- nf.arithmetically_equivalent
- nf.class_number
- nf.class_number_formula
- nf.cm_field
- nf.conductor
- nf.defining_polynomial
- nf.degree
- nf.discriminant
- nf.field_generator
- nf.fundamental_units
- nf.galois_root_discriminant
- nf.generator
- nf.ideal_class_group
- nf.index
- nf.inessential_prime
- nf.integral
- nf.integral_basis
- nf.invariants
- nf.local_algebra
- 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.primitive_element
- nf.rank
- nf.regulator
- nf.ring_of_integers
- nf.root_discriminant
- nf.search_input
- nf.serre_odlyzko_bound
- nf.signature
- nf.torsion
- nf.totally_imaginary
- nf.totally_positive
- nf.totally_real
- nf.unit_group
- nf.unramified_prime
- nf.weil_height
- nf.zk_index
- rcs
- rcs.cande.ec
- rcs.cande.mf.bianchi
- rcs.rigor.ec
- ring.dedekind_domain
- st_group.1.2.A.1.1a.bottom
- st_group.1.2.A.1.1a.top
- st_group.1.2.B.1.1a.bottom
- st_group.1.4.A.1.1a.top
- st_group.1.4.F.48.48a.bottom
- st_group.component_group
- st_group.degree
- lmfdb/artin_representations/math_classes.py (lines 597-599)
- lmfdb/bianchi_modular_forms/bianchi_modular_form.py (line 132)
- lmfdb/bianchi_modular_forms/bianchi_modular_form.py (line 331)
- lmfdb/bianchi_modular_forms/bianchi_modular_form.py (line 708)
- lmfdb/bianchi_modular_forms/bianchi_modular_form.py (line 797)
- lmfdb/bianchi_modular_forms/bianchi_modular_form.py (line 806)
- lmfdb/bianchi_modular_forms/bianchi_modular_form.py (line 818)
- lmfdb/bianchi_modular_forms/bianchi_modular_form.py (line 839)
- lmfdb/ecnf/ecnf_stats.py (lines 86-87)
- lmfdb/ecnf/main.py (line 360)
- lmfdb/ecnf/main.py (line 680)
- lmfdb/half_integral_weight_forms/half_integral_form.py (line 118)
- lmfdb/hilbert_modular_forms/hilbert_modular_form.py (line 140)
- lmfdb/hilbert_modular_forms/hilbert_modular_form.py (line 636)
- lmfdb/lfunctions/Lfunction.py (line 1234)
- lmfdb/number_fields/__init__.py (line 12)
- lmfdb/number_fields/number_field.py (line 126)
- lmfdb/number_fields/number_field.py (line 761)
- lmfdb/number_fields/number_field.py (line 1026)
- lmfdb/number_fields/number_field.py (line 1097)
- 2018-07-07 19:29:57 by Alina Bucur (Reviewed)