Number field data - 4.4.127449.1

Formats: - HTML - YAML - JSON - 2026-04-21T08:33:25.262611

• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, -19, 0, 1], 'conductor': 357, 'degree': 4, 'disc_abs': 127449, 'disc_rad': 357, 'disc_sign': 1, 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2, 2, 2], 'galois_label': '4T2', 'galt': 2, 'grd': 18.894443627691185, 'index': 2, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.127449.1', 'local_algs': ['3.2.2.2a1.2', '7.2.2.2a1.2', '17.1.2.1a1.1', '17.1.2.1a1.1'], 'monogenic': -1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 0, 'ramps': [3, 7, 17], 'rd': 18.8944436277, 'regulator': {'__RealLiteral__': 0, 'data': '19.3090034354', 'prec': 44}, 'subfield_mults': [1, 1, 1], 'subfields': ['-4.-1.1', '-5.-1.1', '-89.-1.1'], 'torsion_order': 2, 'unit_signature_rank': 3, 'used_grh': False}
• nf_fields_extra •

  Column	Type
  dirichlet_group	bigint[]
  frobs	jsonb
  label	text
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [1, 188, 356, 169], 'frobs': [[2, [[2, 2]]], [3, [0]], [5, [[2, 2]]], [7, [0]], [11, [[2, 2]]], [13, [[2, 2]]], [17, [0]], [19, [[2, 2]]], [23, [[2, 2]]], [29, [[2, 2]]], [31, [[2, 2]]], [37, [[2, 2]]], [41, [[2, 2]]], [43, [[1, 4]]], [47, [[1, 4]]], [53, [[2, 2]]], [59, [[1, 4]]]], 'label': '4.4.127449.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( a \\)', '\\( \\frac{1}{2} a^{3} - 10 a - \\frac{5}{2} \\)', '\\( a^{3} - 18 a - 4 \\)'], 'unitsGmodule': [[1, 1], [2, 1], [3, 1]], 'unitsType': 'Type I (ii)', 'zk': ['1', 'a', '1/2*a^2 - 1/2*a - 1/2', '1/2*a^3 - 1/2']}