Number field data - 8.2.14206147659.1

Formats: - HTML - YAML - JSON - 2024-06-10T05:23:48.081862

• 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[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	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': [], 'class_number': 1, 'cm': False, 'coeffs': [16, -28, -4, -1, 16, -5, -1, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 14206147659, 'disc_rad': 33, 'disc_sign': -1, 'frobs': [[2, [[2, 3], [1, 2]]], [3, [0]], [5, [[4, 2]]], [7, [[8, 1]]], [11, [0]], [13, [[8, 1]]], [17, [[2, 3], [1, 2]]], [19, [[8, 1]]], [23, [[4, 2]]], [29, [[2, 3], [1, 2]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[2, 3], [1, 2]]], [43, [[8, 1]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 14], 'galois_label': '8T8', 'galt': 8, 'grd': 18.580591723225652, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.14206147659.1', 'local_algs': ['3.8.6.1', '11.8.7.2'], 'monogenic': -1, 'num_ram': 2, 'r2': 3, 'ramps': [3, 11], 'rd': 18.5805917232, 'regulator': {'__RealLiteral__': 0, 'data': '453.969657745', 'prec': 44}, 'res': {'gal': ['144,-576,1044,-1332,1683,-2259,2784,-2901,2554,-1895,1178,-623,286,-109,32,-7,1'], 'sib': ['144,-576,1044,-1332,1683,-2259,2784,-2901,2554,-1895,1178,-623,286,-109,32,-7,1']}, 'subfield_mults': [1, 1], 'subfields': ['-8.-1.1', '-2.5.-4.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{4} a^{7} - \\frac{1}{2} a^{6} - \\frac{1}{2} a^{5} - \\frac{5}{4} a^{4} + \\frac{9}{2} a^{3} + 2 a^{2} - a - 9 \\)', '\\( \\frac{1}{16} a^{7} - \\frac{1}{16} a^{6} - \\frac{1}{2} a^{5} + \\frac{1}{16} a^{4} + \\frac{9}{16} a^{3} + \\frac{17}{8} a^{2} - 3 a - 1 \\)', '\\( \\frac{1}{8} a^{6} + \\frac{3}{8} a^{5} - a^{4} - \\frac{7}{8} a^{3} - \\frac{19}{8} a^{2} + \\frac{17}{4} a - 2 \\)', '\\( \\frac{1}{8} a^{6} + \\frac{1}{8} a^{5} - \\frac{3}{8} a^{3} - \\frac{1}{8} a^{2} + \\frac{1}{4} a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a', '1/4*a^5 - 1/2*a^3 - 1/4*a^2', '1/8*a^6 - 1/8*a^5 + 1/8*a^3 + 1/8*a^2 + 1/4*a', '1/16*a^7 - 1/16*a^6 + 1/16*a^4 - 7/16*a^3 - 3/8*a^2']}