Number field data - 6.0.64827.1

Formats: - HTML - YAML - JSON - 2026-07-22T04:13:09.966733

• 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[]
  maxp	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': True, 'coeffs': [1, -2, 5, 0, 3, -1, 1], 'conductor': 21, 'degree': 6, 'disc_abs': 64827, 'disc_rad': 21, 'disc_sign': -1, 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 4], 'galois_label': '6T1', 'galt': 1, 'grd': 6.338103410186692, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '6.0.64827.1', 'local_algs': ['3.3.2.3a1.2', '7.1.3.2a1.1', '7.1.3.2a1.1'], 'maximal_cm_subfield': [1, -2, 5, 0, 3, -1, 1], 'maxp': 7, 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 3, 'ramps': [3, 7], 'rd': 6.33810341019, 'regulator': {'__RealLiteral__': 0, 'data': '2.10181872849', 'prec': 44}, 'relative_class_number': 1, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '1.-2.-1.1'], 'torsion_order': 6, 'unit_signature_rank': 0, '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': [16, 1, 2, 4, 8, 11], 'frobs': [[2, [[6, 1]]], [3, [0]], [5, [[6, 1]]], [7, [0]], [11, [[6, 1]]], [13, [[1, 6]]], [17, [[6, 1]]], [19, [[3, 2]]], [23, [[6, 1]]], [29, [[2, 3]]], [31, [[3, 2]]], [37, [[3, 2]]], [41, [[2, 3]]], [43, [[1, 6]]], [47, [[6, 1]]], [53, [[6, 1]]], [59, [[6, 1]]]], 'label': '6.0.64827.1', 'res': {'sex': ['0,1', '1,-1,1', '1,-2,-1,1']}, 'torsion_gen': '\\( \\frac{6}{13} a^{5} - \\frac{5}{13} a^{4} + \\frac{15}{13} a^{3} + \\frac{9}{13} a^{2} + \\frac{25}{13} a + \\frac{3}{13} \\)', 'units': ['\\( \\frac{7}{13} a^{5} - \\frac{8}{13} a^{4} + \\frac{24}{13} a^{3} - \\frac{9}{13} a^{2} + \\frac{40}{13} a - \\frac{16}{13} \\)', '\\( \\frac{5}{13} a^{5} - \\frac{2}{13} a^{4} + \\frac{6}{13} a^{3} + \\frac{14}{13} a^{2} + \\frac{10}{13} a - \\frac{4}{13} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/13*a^5 - 3/13*a^4 - 4/13*a^3 - 5/13*a^2 + 2/13*a - 6/13']}