Number field data - 7.7.35271352782961.1

Formats: - HTML - YAML - JSON - 2025-04-29T11:02:50.208602

• 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[]
  minimal_sibling	numeric[]
  monogenic	smallint
  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': [-171, 740, 1563, 809, 27, -54, -3, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 35271352782961, 'disc_rad': 2437, 'disc_sign': 1, 'frobs': [[2, [[3, 2], [1, 1]]], [3, [[3, 2], [1, 1]]], [5, [[3, 2], [1, 1]]], [7, [[3, 2], [1, 1]]], [11, [[7, 1]]], [13, [[3, 2], [1, 1]]], [17, [[7, 1]]], [19, [[1, 7]]], [23, [[3, 2], [1, 1]]], [29, [[3, 2], [1, 1]]], [31, [[3, 2], [1, 1]]], [37, [[3, 2], [1, 1]]], [41, [[7, 1]]], [43, [[3, 2], [1, 1]]], [47, [[7, 1]]], [53, [[3, 2], [1, 1]]], [59, [[7, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [14], 'galois_label': '7T3', 'galt': 3, 'grd': 181.09384346420086, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.7.35271352782961.1', 'local_algs': ['m2437.1.1.0', 'm2437.3.1.2', 'm2437.3.1.2'], 'monogenic': 0, 'num_ram': 1, 'r2': 0, 'ramps': [2437], 'rd': 86.1680007529, 'regulator': {'__RealLiteral__': 0, 'data': '135074.477609', 'prec': 44}, 'res': {'gal': ['-2850417,-13599720,304447716,-641707484,-909663272,1144772550,998224474,-693064065,-483795132,215806748,122406944,-39824016,-17290460,4539604,1359753,-310364,-55416,11460,992,-186,-6,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{76} a^{6} - \\frac{1}{19} a^{5} - \\frac{23}{38} a^{4} + \\frac{49}{76} a^{3} + \\frac{156}{19} a^{2} + \\frac{1407}{76} a + \\frac{55}{4} \\)', '\\( \\frac{3}{38} a^{6} - \\frac{25}{76} a^{5} - \\frac{289}{76} a^{4} + \\frac{499}{76} a^{3} + \\frac{1016}{19} a^{2} + \\frac{2221}{38} a + \\frac{17}{4} \\)', '\\( \\frac{1}{19} a^{6} - \\frac{1}{4} a^{5} - \\frac{185}{76} a^{4} + \\frac{431}{76} a^{3} + \\frac{1253}{38} a^{2} + \\frac{1051}{38} a - \\frac{17}{4} \\)', '\\( \\frac{79}{152} a^{6} - \\frac{89}{38} a^{5} - \\frac{1849}{76} a^{4} + \\frac{7739}{152} a^{3} + \\frac{6375}{19} a^{2} + \\frac{42581}{152} a - \\frac{451}{8} \\)', '\\( \\frac{51}{152} a^{6} - \\frac{61}{38} a^{5} - \\frac{1167}{76} a^{4} + \\frac{5455}{152} a^{3} + \\frac{8059}{38} a^{2} + \\frac{26669}{152} a - \\frac{283}{8} \\)', '\\( \\frac{15}{19} a^{6} - \\frac{119}{38} a^{5} - \\frac{1481}{38} a^{4} + \\frac{2215}{38} a^{3} + \\frac{10492}{19} a^{2} + \\frac{12997}{19} a + \\frac{269}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^2 - 1/2*a - 1/2', '1/76*a^5 + 13/76*a^4 + 23/76*a^3 - 4/19*a^2 - 7/19*a + 1/4', '1/152*a^6 + 3/76*a^4 + 65/152*a^3 - 6/19*a^2 + 3/152*a - 1/8']}