Number field data - 8.0.18832398664625.3

Formats: - HTML - YAML - JSON - 2026-03-14T23:39:31.924853

• 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
  used_grh	boolean

  
  {'class_group': [4], 'class_number': 4, 'cm': False, 'coeffs': [1600, -2560, 2208, -1008, 200, 20, -15, -1, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 18832398664625, 'disc_rad': 455, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 16, 28], 'galois_label': '8T17', 'galt': 17, 'grd': 83.45972637422375, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '8.0.18832398664625.3', 'local_algs': ['5.1.1.0a1.1', '5.1.1.0a1.1', '5.1.1.0a1.1', '5.1.1.0a1.1', '5.1.4.3a1.3', '7.4.2.4a1.2', '13.1.8.7a1.4'], 'maximal_cm_subfield': [23, -1, 1], 'monogenic': -1, 'narrow_class_group': [4], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 4, 'ramps': [5, 7, 13], 'rd': 45.6418463796, 'regulator': {'__RealLiteral__': 0, 'data': '3122.0067281', 'prec': 40}, 'subfield_mults': [1, 1], 'subfields': ['23.-1.1', '100.6.-5.-2.1'], 'torsion_order': 2, '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[]
  unit_signature_rank	smallint
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [], 'frobs': [[2, [[2, 4]]], [3, [[8, 1]]], [5, [0]], [7, [0]], [11, [[8, 1]]], [13, [0]], [17, [[8, 1]]], [19, [[4, 1], [1, 4]]], [23, [[4, 1], [2, 2]]], [29, [[2, 2], [1, 4]]], [31, [[4, 1], [2, 2]]], [37, [[4, 2]]], [41, [[4, 1], [2, 2]]], [43, [[4, 1], [1, 4]]], [47, [[2, 2], [1, 4]]], [53, [[4, 1], [1, 4]]], [59, [[4, 1], [2, 2]]]], 'label': '8.0.18832398664625.3', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'unit_signature_rank': 0, 'units': ['\\( \\frac{63}{2560} a^{7} + \\frac{11}{2560} a^{6} + \\frac{193}{2560} a^{5} + \\frac{2657}{1280} a^{4} + \\frac{2433}{640} a^{3} - \\frac{11791}{320} a^{2} + \\frac{2077}{32} a - \\frac{1177}{16} \\)', '\\( \\frac{577}{2560} a^{7} + \\frac{5877}{2560} a^{6} - \\frac{1057}{2560} a^{5} - \\frac{46513}{1280} a^{4} - \\frac{5497}{640} a^{3} + \\frac{19683}{64} a^{2} - \\frac{98353}{160} a + \\frac{10593}{16} \\)', '\\( \\frac{9}{2560} a^{7} - \\frac{7}{512} a^{6} + \\frac{183}{2560} a^{5} - \\frac{713}{1280} a^{4} + \\frac{1223}{640} a^{3} - \\frac{1417}{320} a^{2} + \\frac{823}{160} a - \\frac{63}{16} \\)'], 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2 - 1/2*a', '1/4*a^4 - 1/4*a^3 + 1/4*a^2', '1/16*a^5 - 1/16*a^4 + 1/16*a^3 - 1/4*a^2 - 1/2', '1/160*a^6 - 3/160*a^5 + 11/160*a^4 + 9/80*a^3 - 1/10*a^2 - 7/20*a - 1/2', '1/2560*a^7 + 1/512*a^6 + 47/2560*a^5 - 57/1280*a^4 + 47/640*a^3 + 47/320*a^2 + 7/160*a - 7/16']}