Number field data - 12.0.54780521154084864.58

Formats: - HTML - YAML - JSON - 2026-01-27T15:53:36.388088

• 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': [54, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 54780521154084864, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 6]]], [7, [[12, 1]]], [11, [[2, 5], [1, 2]]], [13, [[12, 1]]], [17, [[2, 5], [1, 2]]], [19, [[3, 4]]], [23, [[2, 6]]], [29, [[2, 6]]], [31, [[4, 3]]], [37, [[12, 1]]], [41, [[2, 5], [1, 2]]], [43, [[1, 12]]], [47, [[2, 6]]], [53, [[2, 6]]], [59, [[2, 5], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [70, 28], 'galois_label': '12T12', 'galt': 12, 'grd': 27.20480503537909, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 58, 'label': '12.0.54780521154084864.58', 'local_algs': ['2.1.12.35a1.19', '3.1.6.7a2.2', '3.2.3.6a2.1'], 'maximal_cm_subfield': [2, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 6, 'ramps': [2, 3], 'rd': 24.8247859952, 'regulator': {'__RealLiteral__': 0, 'data': '7606.11042789', 'prec': 44}, 'res': {'gal': ['36,0,144,0,216,0,624,0,1644,0,1560,0,1108,0,2256,0,2040,0,512,0,90,0,12,0,1'], 'sib': ['-2,0,0,0,0,0,44,0,0,0,0,0,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['2.0.1', '-2.0.0.1', '6.0.4.0.1', '2.0.0.0.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{45} a^{10} - \\frac{1}{45} a^{4} + 1 \\)', '\\( \\frac{1}{15} a^{10} + \\frac{7}{15} a^{4} - a^{2} + 1 \\)', '\\( \\frac{4}{135} a^{11} + \\frac{1}{45} a^{10} - \\frac{2}{45} a^{9} - \\frac{2}{15} a^{7} + \\frac{1}{5} a^{6} + \\frac{43}{135} a^{5} - \\frac{23}{45} a^{4} + \\frac{1}{45} a^{3} + \\frac{1}{15} a + \\frac{7}{5} \\)', '\\( \\frac{2}{15} a^{9} - \\frac{2}{5} a^{6} + \\frac{14}{15} a^{3} + \\frac{1}{5} \\)', '\\( \\frac{2}{135} a^{11} + \\frac{1}{45} a^{10} - \\frac{1}{45} a^{9} - \\frac{1}{15} a^{7} + \\frac{1}{5} a^{6} - \\frac{46}{135} a^{5} + \\frac{22}{45} a^{4} - \\frac{22}{45} a^{3} + a^{2} - \\frac{22}{15} a + \\frac{7}{5} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/5*a^6 + 2/5', '1/5*a^7 + 2/5*a', '1/15*a^8 + 7/15*a^2', '1/15*a^9 + 7/15*a^3', '1/45*a^10 + 22/45*a^4', '1/135*a^11 + 1/45*a^9 + 1/15*a^7 - 23/135*a^5 + 22/45*a^3 + 7/15*a']}