Number field data - 6.2.440711081.1

Formats: - HTML - YAML - JSON - 2024-04-28T13:59:23.143377

• 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': [-72, 4, 44, -13, -2, -1, 1], 'conductor': 0, 'degree': 6, 'dirichlet_group': [], 'disc_abs': 440711081, 'disc_rad': 761, 'disc_sign': 1, 'frobs': [[2, [[3, 2]]], [3, [[4, 1], [1, 2]]], [5, [[3, 2]]], [7, [[2, 3]]], [11, [[4, 1], [1, 2]]], [13, [[4, 1], [1, 2]]], [17, [[3, 2]]], [19, [[2, 2], [1, 2]]], [23, [[2, 2], [1, 2]]], [29, [[3, 2]]], [31, [[2, 3]]], [37, [[3, 2]]], [41, [[3, 2]]], [43, [[4, 1], [1, 2]]], [47, [[3, 2]]], [53, [[2, 3]]], [59, [[3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '6T8', 'galt': 8, 'grd': 27.586228448267445, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '6.2.440711081.1', 'local_algs': ['m761.2.1.1', 'm761.2.2.2'], 'minimal_sibling': [1, 2, 1, -1, 1], 'monogenic': 0, 'num_ram': 1, 'r2': 2, 'ramps': [761], 'rd': 27.5862284483, 'regulator': {'__RealLiteral__': 0, 'data': '102.117682633', 'prec': 44}, 'res': {'gal': ['1,0,55,0,612,0,2954,0,4864,0,-2276,0,-3347,0,1112,0,538,0,-175,0,-25,0,13,0,1'], 'sex': ['0,1', '0,1', '1,2,1,-1,1'], 'sib': ['1,2,1,-1,1', '-1,0,-6,0,-1,0,1', '139,-420,109,766,-721,332,49,-214,157,-80,27,-6,1', '2260,263,941,44,207,-9,23,-2,1', '8,-36,96,-177,226,-204,139,-87,57,-27,8,-3,1']}, 'subfield_mults': [1], 'subfields': ['-1.-6.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{28} a^{5} + \\frac{3}{28} a^{4} - \\frac{1}{14} a^{3} - \\frac{13}{28} a^{2} - \\frac{1}{7} a + \\frac{23}{7} \\)', '\\( \\frac{1}{28} a^{5} + \\frac{3}{28} a^{4} - \\frac{1}{14} a^{3} - \\frac{13}{28} a^{2} - \\frac{1}{7} a + \\frac{37}{7} \\)', '\\( 4 a^{5} - \\frac{60}{7} a^{4} + \\frac{12}{7} a^{3} - \\frac{379}{7} a^{2} + \\frac{1668}{7} a - \\frac{1781}{7} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/14*a^4 - 3/14*a^3 + 1/7*a^2 + 3/14*a + 3/7', '1/28*a^5 - 1/28*a^4 + 5/14*a^3 + 1/4*a^2 + 3/7*a + 3/7']}