Number field data - 12.0.25389989167104000000.1

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• 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': [6], 'class_number': 6, 'cm': True, 'coeffs': [64, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 25389989167104000000, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[2, 6]]], [11, [[6, 2]]], [13, [[2, 6]]], [17, [[2, 4], [1, 4]]], [19, [[3, 4]]], [23, [[2, 6]]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[2, 6]]], [41, [[6, 2]]], [43, [[2, 6]]], [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, 36, 12], 'galois_label': '12T10', 'galt': 10, 'grd': 41.40523078218084, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.0.25389989167104000000.1', 'local_algs': ['2.1.6.11a1.1', '2.1.6.11a1.1', '3.1.6.9a2.3', '3.1.6.9a2.3', '5.2.2.2a1.2', '5.2.2.2a1.2', '5.2.2.2a1.2'], 'maximal_cm_subfield': [64, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 1], 'minimal_sibling': [4, 0, -72, 0, 1272, 0, -428, 0, 108, 0, -12, 0, 1], 'monogenic': 0, 'narrow_class_group': [6], 'narrow_class_number': 6, 'num_ram': 3, 'r2': 6, 'ramps': [2, 3, 5], 'rd': 41.4052307822, 'regulator': {'__RealLiteral__': 0, 'data': '51657.6426592', 'prec': 44}, 'relative_class_number': 3, 'res': {'gal': ['2601,3672,12528,-16488,1881,-85788,188436,-161676,115452,-138852,159348,-141576,110359,-81924,59538,-41908,27432,-15984,8046,-3432,1221,-352,78,-12,1'], 'sib': ['4,0,-72,0,1272,0,-428,0,108,0,-12,0,1', '4096,0,0,0,0,0,122,0,0,0,0,0,1', '900,0,1080,0,936,0,372,0,108,0,12,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['-30.0.1', '4.-1.1', '2.0.1', '-14.-12.0.1', '6.-12.13.-2.1', '-30.0.36.0.-12.0.1', '64.0.0.-14.0.0.1', '2.0.36.0.12.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{16} a^{10} - \\frac{1}{4} a^{8} + \\frac{1}{8} a^{4} + \\frac{5}{2} a^{2} - 1 \\)', '\\( \\frac{1}{32} a^{11} + \\frac{1}{16} a^{10} - \\frac{7}{16} a^{5} - \\frac{7}{8} a^{4} - a^{2} - a - 3 \\)', '\\( \\frac{5}{32} a^{11} - \\frac{1}{4} a^{10} + \\frac{1}{8} a^{9} + \\frac{1}{4} a^{8} - \\frac{1}{2} a^{7} - \\frac{19}{16} a^{5} + \\frac{5}{2} a^{4} - \\frac{11}{4} a^{3} + \\frac{1}{2} a^{2} + 2 a + 1 \\)', '\\( \\frac{1}{32} a^{11} - \\frac{1}{16} a^{10} - \\frac{7}{16} a^{5} + \\frac{7}{8} a^{4} + a^{2} - a + 3 \\)', '\\( \\frac{3}{32} a^{11} + \\frac{1}{16} a^{10} - \\frac{1}{2} a^{7} - \\frac{5}{16} a^{5} - \\frac{7}{8} a^{4} - a^{2} + 4 a + 3 \\)'], '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', '1/8*a^9 + 1/4*a^3', '1/16*a^10 + 1/8*a^4', '1/32*a^11 - 7/16*a^5']}