Number field data - 9.1.134573648589.1

Formats: - HTML - YAML - JSON - 2024-04-19T16:22:23.416964

• 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': [], 'class_number': 1, 'cm': False, 'coeffs': [9, 12, -45, 31, -30, 27, -5, 9, 0, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 134573648589, 'disc_rad': 87, 'disc_sign': 1, 'frobs': [[2, [[6, 1], [3, 1]]], [3, [0]], [5, [[4, 1], [3, 1], [2, 1]]], [7, [[9, 1]]], [11, [[6, 1], [3, 1]]], [13, [[9, 1]]], [17, [[6, 1], [3, 1]]], [19, [[3, 1], [2, 3]]], [23, [[4, 1], [3, 1], [2, 1]]], [29, [0]], [31, [[6, 1], [1, 3]]], [37, [[6, 1], [3, 1]]], [41, [[3, 2], [2, 1], [1, 1]]], [43, [[4, 1], [2, 2], [1, 1]]], [47, [[6, 1], [3, 1]]], [53, [[2, 4], [1, 1]]], [59, [[4, 1], [2, 1], [1, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1512, 972], 'galois_label': '9T31', 'galt': 31, 'grd': 45.02357354987992, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.1.134573648589.1', 'local_algs': ['3.1.0.1', '3.2.1.2', '3.6.7.3', '29.1.0.1', '29.2.1.1', '29.2.1.2', '29.4.3.3'], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [3, 29], 'rd': 17.2405499114, 'regulator': {'__RealLiteral__': 0, 'data': '177.351346168', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.2.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{3} a^{6} + 2 a^{4} - \\frac{1}{3} a^{3} + 3 a^{2} - a - 1 \\)', '\\( \\frac{2}{9} a^{8} + \\frac{2}{9} a^{7} + \\frac{17}{9} a^{6} + \\frac{7}{9} a^{5} + \\frac{43}{9} a^{4} - \\frac{5}{9} a^{3} + \\frac{10}{3} a^{2} - \\frac{8}{3} a - 1 \\)', '\\( \\frac{2}{9} a^{8} + \\frac{2}{9} a^{7} + \\frac{20}{9} a^{6} + \\frac{13}{9} a^{5} + \\frac{61}{9} a^{4} + \\frac{19}{9} a^{3} + \\frac{14}{3} a^{2} - \\frac{2}{3} a - 6 \\)', '\\( \\frac{1}{3} a^{8} + \\frac{10}{3} a^{6} - a^{5} + 11 a^{4} - \\frac{19}{3} a^{3} + \\frac{35}{3} a^{2} - 10 a - 2 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/3*a^5 - 1/3*a^2', '1/3*a^6 - 1/3*a^3', '1/3*a^7 - 1/3*a^4', '1/9*a^8 + 1/9*a^7 + 1/9*a^6 - 1/9*a^5 - 1/9*a^4 - 4/9*a^3 - 1/3*a^2 - 1/3*a']}