Number field data - 8.0.60886809.1

Formats: - HTML - YAML - JSON - 2025-12-04T06:22:15.012208

• 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': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 16, 0, 18, 0, 7, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 60886809, 'disc_rad': 51, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [[4, 2]]], [7, [[3, 2], [1, 2]]], [11, [[2, 4]]], [13, [[3, 2], [1, 2]]], [17, [0]], [19, [[3, 2], [1, 2]]], [23, [[4, 2]]], [29, [[2, 4]]], [31, [[3, 2], [1, 2]]], [37, [[3, 2], [1, 2]]], [41, [[2, 4]]], [43, [[3, 2], [1, 2]]], [47, [[2, 4]]], [53, [[2, 4]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [18, 16], 'galois_label': '8T14', 'galt': 14, 'grd': 15.070935874553902, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.0.60886809.1', 'local_algs': ['3.2.4.6a1.2', '17.2.1.0a1.1', '17.2.3.4a1.2'], 'maximal_cm_subfield': [1, -1, 1], 'minimal_sibling': [1, -4, 0, -1, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 4, 'ramps': [3, 17], 'rd': 9.39864837017, 'regulator': {'__RealLiteral__': 0, 'data': '10.543427475', 'prec': 40}, 'res': {'gal': ['1,-12,70,-264,730,-1602,2936,-4593,6118,-6852,6337,-4587,2075,309,-1589,1464,-575,-195,479,-417,253,-117,40,-9,1'], 'sib': ['-17,0,0,-1,3,-3,1', '-3,0,21,0,13,0,-17,0,3,0,-2,0,1', '1,-4,0,-1,1', '1,0,7,0,8,0,16,0,8,0,7,0,1', '2,-5,12,-15,10,-3,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '1.-4.0.-1.1'], 'torsion_gen': '\\( \\frac{1}{2} a^{5} + \\frac{5}{2} a^{3} + \\frac{7}{2} a + \\frac{1}{2} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{1}{2} a^{7} + 3 a^{5} - \\frac{1}{2} a^{4} + \\frac{13}{2} a^{3} - \\frac{3}{2} a^{2} + \\frac{9}{2} a - 1 \\)', '\\( \\frac{1}{2} a^{7} + 3 a^{5} + \\frac{1}{2} a^{4} + \\frac{13}{2} a^{3} + \\frac{3}{2} a^{2} + \\frac{9}{2} a + 1 \\)', '\\( \\frac{1}{2} a^{6} + \\frac{5}{2} a^{4} + \\frac{7}{2} a^{2} + \\frac{1}{2} a \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^3 - 1/2', '1/2*a^5 - 1/2*a^3 - 1/2*a - 1/2', '1/2*a^6 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^7 - 1/2*a^2 - 1/2*a - 1/2']}