Number field data - 8.2.4286875.1

Formats: - HTML - YAML - JSON - 2025-05-17T08:30:30.134541

• 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
  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': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 2, 2, -1, -2, 1, 0, -1, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 4286875, 'disc_rad': 95, 'disc_sign': -1, 'frobs': [[2, [[8, 1]]], [3, [[8, 1]]], [5, [0]], [7, [[2, 4]]], [11, [[4, 2]]], [13, [[8, 1]]], [17, [[2, 4]]], [19, [0]], [23, [[2, 4]]], [29, [[2, 3], [1, 2]]], [31, [[2, 3], [1, 2]]], [37, [[8, 1]]], [41, [[2, 3], [1, 2]]], [43, [[2, 4]]], [47, [[2, 4]]], [53, [[8, 1]]], [59, [[2, 3], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 8], 'galois_label': '8T6', 'galt': 6, 'grd': 9.746794344808963, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.4286875.1', 'local_algs': ['5.4.2.1', '5.4.2.1', '19.2.0.1', '19.2.1.1', '19.4.2.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 3, 'ramps': [5, 19], 'rd': 6.74555367758, 'regulator': {'__RealLiteral__': 0, 'data': '0.831403828897', 'prec': 47}, 'res': {'gal': ['1,-8,34,-98,221,-416,654,-839,869,-730,509,-304,160,-73,27,-7,1'], 'sib': ['1,1,-1,-4,1,4,-1,-1,1', '1,-8,34,-98,221,-416,654,-839,869,-730,509,-304,160,-73,27,-7,1']}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.-1.2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{6}{17} a^{7} - \\frac{7}{17} a^{6} + \\frac{4}{17} a^{5} - \\frac{6}{17} a^{4} - \\frac{11}{17} a^{3} - \\frac{7}{17} a^{2} - \\frac{1}{17} a + \\frac{15}{17} \\)', '\\( \\frac{1}{17} a^{7} - \\frac{4}{17} a^{6} - \\frac{5}{17} a^{5} - \\frac{1}{17} a^{4} + \\frac{1}{17} a^{3} - \\frac{4}{17} a^{2} + \\frac{14}{17} a + \\frac{11}{17} \\)', '\\( a \\)', '\\( \\frac{12}{17} a^{7} - \\frac{14}{17} a^{6} + \\frac{8}{17} a^{5} + \\frac{5}{17} a^{4} - \\frac{22}{17} a^{3} - \\frac{14}{17} a^{2} + \\frac{15}{17} a + \\frac{13}{17} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/17*a^7 - 4/17*a^6 - 5/17*a^5 - 1/17*a^4 + 1/17*a^3 - 4/17*a^2 - 3/17*a - 6/17']}