Number field data - 12.0.44767018745856.2

Formats: - HTML - YAML - JSON - 2025-11-17T01:50:57.383862

• 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': [4, 0, 0, 0, 4, 0, 4, 0, 4, 0, 2, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 44767018745856, 'disc_rad': 66, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 2]]], [7, [[2, 6]]], [11, [0]], [13, [[2, 6]]], [17, [[2, 6]]], [19, [[2, 4], [1, 4]]], [23, [[6, 2]]], [29, [[2, 6]]], [31, [[6, 2]]], [37, [[6, 2]]], [41, [[2, 6]]], [43, [[2, 4], [1, 4]]], [47, [[2, 6]]], [53, [[2, 6]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [44, 12, 12], 'galois_label': '12T10', 'galt': 10, 'grd': 20.471293992310418, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '12.0.44767018745856.2', 'local_algs': ['2.2.6.22a1.1', '3.3.2.3a1.2', '3.3.2.3a1.2', '11.2.1.0a1.1', '11.2.1.0a1.1', '11.2.2.2a1.2', '11.2.2.2a1.2'], 'maximal_cm_subfield': [4, 0, -2, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 6, 'ramps': [2, 3, 11], 'rd': 13.7271331986, 'regulator': {'__RealLiteral__': 0, 'data': '190.610034603', 'prec': 44}, 'res': {'gal': ['16,0,64,0,176,0,288,0,320,0,-56,0,-24,0,112,0,4,0,-16,0,0,0,-2,0,1'], 'sib': ['16,0,152,0,412,0,226,0,64,0,12,0,1', '484,0,440,0,268,0,76,0,16,0,6,0,1', '64,0,0,0,0,0,-38,0,0,0,0,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['2.0.1', '-6.0.1', '1.-1.1', '1.1.-1.1', '4.0.-2.0.1', '-54.0.0.0.6.0.1', '2.0.0.0.-2.0.1', '1.1.2.-3.0.-1.1'], 'torsion_gen': '\\( -\\frac{1}{4} a^{8} - \\frac{1}{2} a^{6} - a^{4} - \\frac{1}{2} a^{2} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{1}{4} a^{10} + \\frac{1}{2} a^{8} + a^{6} + \\frac{1}{2} a^{4} - 1 \\)', '\\( \\frac{1}{2} a^{6} + a^{4} + a^{2} \\)', '\\( \\frac{1}{4} a^{8} + \\frac{1}{2} a^{6} + a^{4} + \\frac{1}{2} a^{2} - a \\)', '\\( \\frac{1}{4} a^{8} - \\frac{1}{2} a^{2} + a \\)', '\\( \\frac{1}{4} a^{11} - \\frac{1}{4} a^{10} + \\frac{1}{4} a^{9} - \\frac{1}{4} a^{8} + \\frac{1}{2} a^{7} - \\frac{1}{2} a^{5} + \\frac{1}{2} a^{4} - \\frac{1}{2} a^{3} + \\frac{3}{2} a^{2} - 2 a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6', '1/2*a^7', '1/4*a^8 - 1/2*a^2', '1/4*a^9 - 1/2*a^3', '1/4*a^10 - 1/2*a^4', '1/4*a^11 - 1/2*a^5']}