Number field data - 8.0.58451728309129.1

Formats: - HTML - YAML - JSON - 2025-10-24T09:51:10.349555

• 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': [74, -75, 158, -158, 99, -37, 17, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 58451728309129, 'disc_rad': 197, 'disc_sign': 1, 'frobs': [[2, [[7, 1], [1, 1]]], [3, [[7, 1], [1, 1]]], [5, [[7, 1], [1, 1]]], [7, [[7, 1], [1, 1]]], [11, [[7, 1], [1, 1]]], [13, [[7, 1], [1, 1]]], [17, [[7, 1], [1, 1]]], [19, [[2, 4]]], [23, [[7, 1], [1, 1]]], [29, [[7, 1], [1, 1]]], [31, [[7, 1], [1, 1]]], [37, [[7, 1], [1, 1]]], [41, [[7, 1], [1, 1]]], [43, [[7, 1], [1, 1]]], [47, [[7, 1], [1, 1]]], [53, [[7, 1], [1, 1]]], [59, [[7, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [48], 'galois_label': '8T25', 'galt': 25, 'grd': 92.61585422390594, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.0.58451728309129.1', 'local_algs': ['197.1.1.0a1.1', '197.1.7.6a1.1'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 4, 'ramps': [197], 'rd': 52.5835217818, 'regulator': {'__RealLiteral__': 0, 'data': '9937.30836324', 'prec': 44}, 'res': {'sib': ['-100489,0,1191,0,59427,0,15181,0,-2941,0,-857,0,6,0,1', '6889,0,-217883,0,-1656713,0,-3864855,0,-4193060,0,-1919280,0,-90461,0,611811,0,169018,0,-143484,0,-26571,0,9809,0,-319,0,9,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{7972}{35543} a^{7} + \\frac{10074}{35543} a^{6} + \\frac{150925}{35543} a^{5} + \\frac{93750}{35543} a^{4} + \\frac{729709}{35543} a^{3} + \\frac{79875}{35543} a^{2} + \\frac{374174}{35543} a - \\frac{32543}{35543} \\)', '\\( \\frac{888839}{35543} a^{7} - \\frac{2282836}{35543} a^{6} + \\frac{10545486}{35543} a^{5} - \\frac{31268119}{35543} a^{4} + \\frac{45834794}{35543} a^{3} - \\frac{36240033}{35543} a^{2} + \\frac{23584177}{35543} a - \\frac{14049979}{35543} \\)', '\\( \\frac{19965}{35543} a^{7} + \\frac{10650}{35543} a^{6} + \\frac{50745}{35543} a^{5} + \\frac{259763}{35543} a^{4} - \\frac{563495}{35543} a^{3} + \\frac{756880}{35543} a^{2} - \\frac{292027}{35543} a + \\frac{423739}{35543} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/35543*a^7 - 15648/35543*a^6 + 8441/35543*a^5 + 9865/35543*a^4 + 15558/35543*a^3 + 13381/35543*a^2 - 10698/35543*a + 8846/35543']}