Number field data - 8.8.370818940928000.1

Formats: - HTML - YAML - JSON - 2025-12-03T23:48:34.061782

• 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': [2], 'class_number': 2, 'cm': False, 'coeffs': [980, 0, -1672, 0, 502, 0, -44, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 370818940928000, 'disc_rad': 290, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[8, 1]]], [5, [0]], [7, [[2, 3], [1, 2]]], [11, [[2, 4]]], [13, [[2, 3], [1, 2]]], [17, [[8, 1]]], [19, [[2, 4]]], [23, [[2, 3], [1, 2]]], [29, [0]], [31, [[2, 4]]], [37, [[8, 1]]], [41, [[2, 4]]], [43, [[8, 1]]], [47, [[8, 1]]], [53, [[2, 3], [1, 2]]], [59, [[1, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [44, 8, 8], 'galois_label': '8T6', 'galt': 6, 'grd': 81.00586972196002, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.8.370818940928000.1', 'local_algs': ['2.2.4.22a1.72', '5.1.2.1a1.2', '5.2.1.0a1.1', '5.2.2.2a1.2', '29.1.2.1a1.1', '29.1.2.1a1.1', '29.1.2.1a1.1', '29.1.2.1a1.1'], 'minimal_sibling': [2900, 0, -1880, 0, 414, 0, -36, 0, 1], 'monogenic': 0, 'narrow_class_group': [4], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 29], 'rd': 66.2438002063, 'regulator': {'__RealLiteral__': 0, 'data': '42030.7472431', 'prec': 44}, 'res': {'gal': ['55696,0,-225632,0,343176,0,-249072,0,91440,0,-17288,0,1626,0,-68,0,1'], 'sib': ['2900,0,-1880,0,414,0,-36,0,1']}, 'subfield_mults': [1, 1], 'subfields': ['-7.-1.1', '20.0.-14.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{95} a^{6} - \\frac{77}{190} a^{4} + \\frac{314}{95} a^{2} - \\frac{46}{19} \\)', '\\( \\frac{16}{1235} a^{6} - \\frac{1327}{2470} a^{4} + \\frac{6449}{1235} a^{2} - \\frac{2788}{247} \\)', '\\( \\frac{37}{17290} a^{7} - \\frac{1187}{17290} a^{5} + \\frac{1629}{8645} a^{3} + \\frac{1809}{1729} a - 1 \\)', '\\( \\frac{37}{17290} a^{7} - \\frac{1187}{17290} a^{5} + \\frac{1629}{8645} a^{3} + \\frac{1809}{1729} a + 1 \\)', '\\( \\frac{58}{8645} a^{7} + \\frac{29}{2470} a^{6} - \\frac{2328}{8645} a^{5} - \\frac{582}{1235} a^{4} + \\frac{19827}{8645} a^{3} + \\frac{4648}{1235} a^{2} - \\frac{4796}{1729} a - \\frac{705}{247} \\)', '\\( \\frac{79}{17290} a^{7} - \\frac{3}{2470} a^{6} - \\frac{3469}{17290} a^{5} + \\frac{163}{2470} a^{4} + \\frac{18198}{8645} a^{3} - \\frac{566}{1235} a^{2} - \\frac{8334}{1729} a + \\frac{107}{247} \\)', '\\( \\frac{174}{8645} a^{7} + \\frac{1}{19} a^{6} - \\frac{6984}{8645} a^{5} - \\frac{77}{38} a^{4} + \\frac{59481}{8645} a^{3} + \\frac{295}{19} a^{2} - \\frac{7472}{1729} a - \\frac{154}{19} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4', '1/2*a^5', '1/2470*a^6 - 233/1235*a^4 - 223/1235*a^2 - 118/247', '1/17290*a^7 + 3239/17290*a^5 - 3928/8645*a^3 + 376/1729*a']}