Number field data - 8.2.1783963098021888.55

Formats: - HTML - YAML - JSON - 2025-12-04T00:32:20.257685

• 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': [-259308, 0, 19208, 0, 1470, 0, -84, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 1783963098021888, 'disc_rad': 42, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1]]], [7, [0]], [11, [[2, 3], [1, 2]]], [13, [[3, 2], [1, 2]]], [17, [[8, 1]]], [19, [[3, 2], [1, 2]]], [23, [[8, 1]]], [29, [[2, 3], [1, 2]]], [31, [[3, 2], [1, 2]]], [37, [[3, 2], [1, 2]]], [41, [[8, 1]]], [43, [[6, 1], [2, 1]]], [47, [[2, 3], [1, 2]]], [53, [[2, 3], [1, 2]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [132, 88, 24], 'galois_label': '8T23', 'galt': 23, 'grd': 133.3840218795417, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 55, 'label': '8.2.1783963098021888.55', 'local_algs': ['2.2.4.22a1.72', '3.1.2.1a1.1', '3.1.3.5a1.1', '3.1.3.5a1.1', '7.1.2.1a1.2', '7.3.2.3a1.1'], 'minimal_sibling': [-259308, 0, -32928, 0, -1764, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [2, 4], 'narrow_class_number': 8, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 7], 'rd': 80.6163689809, 'regulator': {'__RealLiteral__': 0, 'data': '31279.9046433', 'prec': 44}, 'res': {'ae': ['-259308,0,-32928,0,-1764,0,0,0,1'], 'sib': ['-2657527142592,0,0,0,0,0,113635757312,0,0,0,0,0,5647152,0,0,0,0,0,0,0,0,0,0,0,1', '67240638864,0,-8538493824,0,626833872,0,-58084992,0,3371004,0,-65856,0,1764,0,0,0,1']}, 'subfield_mults': [1], 'subfields': ['7.-2.-3.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3}{7546} a^{6} - \\frac{17}{1078} a^{4} - \\frac{1}{11} a^{2} + \\frac{25}{11} \\)', '\\( \\frac{1}{3773} a^{6} - \\frac{15}{1078} a^{4} - \\frac{1}{77} a^{2} + \\frac{35}{11} \\)', '\\( \\frac{2547493119}{3773} a^{7} + \\frac{7970891000}{3773} a^{6} - \\frac{27007025244}{539} a^{5} - \\frac{84502703000}{539} a^{4} + \\frac{38653104044}{77} a^{3} + \\frac{120942300748}{77} a^{2} + \\frac{196719365140}{11} a + \\frac{615518293237}{11} \\)', '\\( \\frac{750690109804003}{1029} a^{7} + \\frac{18749479081257521}{3773} a^{6} - \\frac{1347763226023091}{49} a^{5} - \\frac{101519991367976484}{539} a^{4} - \\frac{1498983952778502}{7} a^{3} - \\frac{112610759037576132}{77} a^{2} + \\frac{12144580872698954}{3} a + \\frac{304780887328105007}{11} \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/7*a^2', '1/7*a^3', '1/98*a^4', '1/98*a^5', '1/7546*a^6 - 1/539*a^4 + 5/77*a^2 + 1/11', '1/22638*a^7 + 3/1078*a^5 - 2/77*a^3 + 1/33*a']}