Number field data - 8.0.118292480000000.10

Formats: - HTML - YAML - JSON - 2025-12-03T22:46:53.991973

• 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
  dirichlet_group	bigint[]
  frobs	jsonb
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  zk	jsonb

  
  {'class_group': [4], 'class_number': 4, 'cm': False, 'coeffs': [115520, 0, -6080, 0, 440, 0, -40, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 118292480000000, 'disc_rad': 190, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[8, 1]]], [5, [0]], [7, [[8, 1]]], [11, [[4, 2]]], [13, [[8, 1]]], [17, [[8, 1]]], [19, [0]], [23, [[8, 1]]], [29, [[2, 2], [1, 4]]], [31, [[2, 2], [1, 4]]], [37, [[8, 1]]], [41, [[2, 2], [1, 4]]], [43, [[8, 1]]], [47, [[8, 1]]], [53, [[8, 1]]], [59, [[2, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [88, 28, 16], 'galois_label': '8T16', 'galt': 16, 'grd': 119.89692430103565, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 10, 'label': '8.0.118292480000000.10', 'local_algs': ['2.2.4.22a1.72', '5.1.8.7a1.4', '19.1.1.0a1.1', '19.1.1.0a1.1', '19.1.2.1a1.2', '19.1.2.1a1.1', '19.2.1.0a1.1'], 'maximal_cm_subfield': [20, 0, 10, 0, 1], 'monogenic': 0, 'narrow_class_group': [4], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 4, 'ramps': [2, 5, 19], 'rd': 57.427464512, 'regulator': {'__RealLiteral__': 0, 'data': '1459.94767878', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '20.0.10.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3}{21128} a^{6} - \\frac{101}{21128} a^{4} - \\frac{25}{2641} a^{2} - \\frac{82}{139} \\)', '\\( \\frac{791}{42256} a^{7} + \\frac{1451}{21128} a^{6} - \\frac{5117}{10564} a^{5} - \\frac{8031}{5282} a^{4} + \\frac{21579}{5282} a^{3} + \\frac{37207}{2641} a^{2} - \\frac{13822}{139} a - \\frac{72511}{139} \\)', '\\( \\frac{34336453}{42256} a^{7} + \\frac{37209853}{10564} a^{6} - \\frac{144666729}{10564} a^{5} - \\frac{263772845}{5282} a^{4} + \\frac{80217872}{2641} a^{3} + \\frac{228393485}{2641} a^{2} - \\frac{455920070}{139} a - \\frac{2541998251}{139} \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2', '1/4*a^3', '1/8*a^4', '1/8*a^5', '1/42256*a^6 - 457/21128*a^4 + 436/2641*a^2 - 60/139', '1/84512*a^7 + 273/5282*a^5 + 218/2641*a^3 - 30/139*a']}