Number field data - 8.0.16178296651776.7

Formats: - HTML - YAML - JSON - 2024-06-08T14:45:32.182061

• 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': [2], 'class_number': 2, 'cm': False, 'coeffs': [25704, 0, 2520, 0, 252, 0, -4, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 16178296651776, 'disc_rad': 714, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 1], [2, 1]]], [7, [0]], [11, [[3, 2], [2, 1]]], [13, [[4, 2]]], [17, [0]], [19, [[3, 2], [1, 2]]], [23, [[6, 1], [2, 1]]], [29, [[4, 1], [2, 2]]], [31, [[3, 2], [1, 2]]], [37, [[3, 2], [1, 2]]], [41, [[4, 1], [2, 2]]], [43, [[4, 1], [2, 2]]], [47, [[6, 1], [2, 1]]], [53, [[3, 2], [1, 2]]], [59, [[6, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [666, 96, 160, 96], 'galois_label': '8T38', 'galt': 38, 'grd': 400.1577681856893, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 7, 'label': '8.0.16178296651776.7', 'local_algs': ['2.8.21.29', '3.1.0.1', '3.1.0.1', '3.6.3.1', '7.1.0.1', '7.1.0.1', '7.6.5.2', '17.2.1.1', '17.3.0.1', '17.3.0.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 4, 'ramps': [2, 3, 7, 17], 'rd': 44.7833522316, 'regulator': {'__RealLiteral__': 0, 'data': '3855.09578678', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['2.0.2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{23}{130554} a^{6} - \\frac{1205}{130554} a^{4} - \\frac{2087}{21759} a^{2} - \\frac{4111}{7253} \\)', '\\( \\frac{466}{65277} a^{7} - \\frac{5929}{14506} a^{6} + \\frac{178985}{65277} a^{5} - \\frac{77255}{7253} a^{4} + \\frac{623387}{21759} a^{3} - \\frac{726850}{7253} a^{2} + \\frac{1433490}{7253} a - \\frac{3410483}{7253} \\)', '\\( \\frac{590209}{65277} a^{7} + \\frac{24046310}{21759} a^{6} - \\frac{193192873}{65277} a^{5} - \\frac{142543982}{21759} a^{4} + \\frac{979089086}{21759} a^{3} + \\frac{1637506374}{7253} a^{2} - \\frac{6900612950}{7253} a + \\frac{24078605237}{7253} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3', '1/6*a^4 + 1/3*a^2', '1/6*a^5 - 1/6*a^3', '1/261108*a^6 + 4231/130554*a^4 + 7996/21759*a^2 + 699/7253', '1/261108*a^7 + 4231/130554*a^5 - 5767/43518*a^3 + 699/7253*a']}