Number field data - 8.2.4919560343912448.10

Formats: - HTML - YAML - JSON - 2025-12-03T22:42:22.641954

• 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': [2, 4], 'class_number': 8, 'cm': False, 'coeffs': [-10092, 0, -3072, 0, -164, 0, 16, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 4919560343912448, 'disc_rad': 78, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1]]], [7, [[4, 2]]], [11, [[8, 1]]], [13, [0]], [17, [[2, 3], [1, 2]]], [19, [[4, 2]]], [23, [[2, 3], [1, 2]]], [29, [[2, 1], [1, 6]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[8, 1]]], [43, [[2, 2], [1, 4]]], [47, [[8, 1]]], [53, [[2, 3], [1, 2]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [176, 48, 48], 'galois_label': '8T27', 'galt': 27, 'grd': 104.98589220070072, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 10, 'label': '8.2.4919560343912448.10', 'local_algs': ['2.2.4.22a1.72', '3.1.2.1a1.2', '3.1.2.1a1.2', '3.1.4.3a1.2', '13.1.4.3a1.3', '13.1.4.3a1.3'], 'monogenic': 0, 'narrow_class_group': [2, 2, 4], 'narrow_class_number': 16, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 13], 'rd': 91.5146844368, 'regulator': {'__RealLiteral__': 0, 'data': '20336.8803799', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-3.-1.1', '468.0.-78.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{136} a^{6} + \\frac{9}{136} a^{4} - \\frac{105}{68} a^{2} - \\frac{631}{68} \\)', '\\( \\frac{2}{51} a^{6} + \\frac{1}{51} a^{4} - \\frac{106}{17} a^{2} - \\frac{473}{17} \\)', '\\( \\frac{1}{408} a^{6} - \\frac{25}{408} a^{4} - \\frac{103}{68} a^{2} - \\frac{471}{68} \\)', '\\( \\frac{1691924516980166885}{5916} a^{7} - \\frac{25885880612366287}{24} a^{6} + \\frac{12783849508607410573}{1479} a^{5} - \\frac{782354528999707115}{24} a^{4} + \\frac{74972354549649583133}{986} a^{3} - \\frac{1147052010667787479}{4} a^{2} + \\frac{100041273564979754796}{493} a - \\frac{3061196215105733301}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/8*a^4 - 1/2*a^2 + 1/4', '1/8*a^5 - 1/2*a^3 + 1/4*a', '1/408*a^6 - 25/408*a^4 + 33/68*a^2 + 5/68', '1/11832*a^7 - 535/11832*a^5 - 443/1972*a^3 + 39/1972*a']}