Number field data - 8.0.5801854959616.2

Formats: - HTML - YAML - JSON - 2024-12-12T21:42:33.506695

• 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': [2, 10], 'class_number': 20, 'cm': False, 'coeffs': [16, 0, 784, 0, -7, 0, -2, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 5801854959616, 'disc_rad': 194, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 4]]], [5, [[4, 2]]], [7, [[4, 2]]], [11, [[1, 8]]], [13, [[4, 2]]], [17, [[2, 4]]], [19, [[2, 4]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[2, 4]]], [37, [[4, 2]]], [41, [[2, 4]]], [43, [[1, 8]]], [47, [[2, 4]]], [53, [[2, 4]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 4], 'galois_label': '8T4', 'galt': 4, 'grd': 39.395431207184416, 'inessentialp': [3], 'is_galois': True, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '8.0.5801854959616.2', 'local_algs': ['2.4.8.4', '2.4.8.4', '97.4.2.1', '97.4.2.1'], 'minimal_sibling': [22, -12, 6, 0, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 4, 'ramps': [2, 97], 'rd': 39.3954312072, 'regulator': {'__RealLiteral__': 0, 'data': '343.553838059', 'prec': 44}, 'res': {'sib': ['-18,0,-5,0,1', '22,-12,6,0,1']}, 'subfield_mults': [1, 1, 1, 1, 2, 2], 'subfields': ['194.0.1', '2.0.1', '-24.-1.1', '678.44.-43.-2.1', '22.-12.6.0.1', '-18.0.-5.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{13}{5784} a^{7} - \\frac{1}{482} a^{6} - \\frac{11}{723} a^{5} - \\frac{5}{964} a^{4} - \\frac{5}{5784} a^{3} - \\frac{129}{964} a^{2} + \\frac{985}{723} a - \\frac{25}{241} \\)', '\\( \\frac{13}{5784} a^{7} + \\frac{1}{482} a^{6} - \\frac{11}{723} a^{5} + \\frac{5}{964} a^{4} - \\frac{5}{5784} a^{3} + \\frac{129}{964} a^{2} + \\frac{985}{723} a + \\frac{25}{241} \\)', '\\( \\frac{853}{1928} a^{7} - \\frac{116}{723} a^{6} - \\frac{461}{482} a^{5} + \\frac{1973}{2892} a^{4} - \\frac{4629}{1928} a^{3} - \\frac{7997}{2892} a^{2} + \\frac{164541}{482} a - \\frac{67978}{723} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a', '1/2*a^4 - 1/2*a^2', '1/4*a^5 - 1/4*a^4 - 1/4*a^3 + 1/4*a^2', '1/2892*a^6 - 59/1446*a^4 - 779/2892*a^2 - 349/723', '1/5784*a^7 - 59/2892*a^5 - 779/5784*a^3 + 187/723*a']}