Number field data - 8.0.151939915084881.1

Formats: - HTML - YAML - JSON - 2026-04-11T23:53:20.769961

• 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': [2, 6, 6], 'class_number': 72, 'cm': True, 'coeffs': [17623, 5545, 842, 2173, 529, 71, 50, -1, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 151939915084881, 'disc_rad': 231, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 6, 6], 'galois_label': '8T5', 'galt': 5, 'grd': 59.252814612259755, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.151939915084881.1', 'local_algs': ['3.2.4.6a1.3', '7.2.4.6a1.3', '11.2.4.6a1.3'], 'maximal_cm_subfield': [17623, 5545, 842, 2173, 529, 71, 50, -1, 1], 'monogenic': 0, 'narrow_class_group': [2, 6, 6], 'narrow_class_number': 72, 'num_ram': 3, 'r2': 4, 'ramps': [3, 7, 11], 'rd': 59.2528146123, 'regulator': {'__RealLiteral__': 0, 'data': '104.827448547', 'prec': 44}, 'relative_class_number': 72, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-8.-1.1', '-5.-1.1', '-19.-1.1', '-17.37.-16.-1.1'], 'torsion_order': 2, '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': [], 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [[4, 2]]], [7, [0]], [11, [0]], [13, [[4, 2]]], [17, [[1, 8]]], [19, [[4, 2]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[1, 8]]], [41, [[1, 8]]], [43, [[4, 2]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'label': '8.0.151939915084881.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{5745961}{36270630857} a^{7} - \\frac{6527976}{36270630857} a^{6} + \\frac{222373728}{36270630857} a^{5} + \\frac{298263703}{36270630857} a^{4} + \\frac{1372164699}{36270630857} a^{3} + \\frac{7555042615}{36270630857} a^{2} - \\frac{8494818489}{36270630857} a - \\frac{9756958913}{36270630857} \\)', '\\( \\frac{16383577}{36270630857} a^{7} - \\frac{10783786}{36270630857} a^{6} + \\frac{727410945}{36270630857} a^{5} + \\frac{1312883715}{36270630857} a^{4} + \\frac{5457923391}{36270630857} a^{3} + \\frac{24391519775}{36270630857} a^{2} - \\frac{23054803265}{36270630857} a - \\frac{99979153583}{36270630857} \\)', '\\( \\frac{5149937}{36270630857} a^{7} + \\frac{240974}{36270630857} a^{6} + \\frac{89606258}{36270630857} a^{5} + \\frac{396628742}{36270630857} a^{4} - \\frac{230494035}{36270630857} a^{3} - \\frac{38679001}{36270630857} a^{2} + \\frac{5709942646}{36270630857} a - \\frac{5048433697}{36270630857} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/17*a^6 + 5/17*a^5 + 3/17*a^4 - 7/17*a^3 + 1/17*a^2 - 2/17*a + 5/17', '1/36270630857*a^7 + 374998582/36270630857*a^6 + 17017736938/36270630857*a^5 + 14057084747/36270630857*a^4 - 15124706705/36270630857*a^3 + 4190455030/36270630857*a^2 - 10103876566/36270630857*a - 12323908292/36270630857']}