Number field data - 8.2.265847707.1

Formats: - HTML - YAML - JSON - 2024-06-07T05:29:24.232959

• 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
  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': [-1, 4, -12, 18, -7, 1, 3, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 265847707, 'disc_rad': 643, 'disc_sign': -1, 'frobs': [[2, [[8, 1]]], [3, [[8, 1]]], [5, [[2, 3], [1, 2]]], [7, [[6, 1], [2, 1]]], [11, [[8, 1]]], [13, [[8, 1]]], [17, [[8, 1]]], [19, [[8, 1]]], [23, [[3, 2], [1, 2]]], [29, [[6, 1], [2, 1]]], [31, [[3, 2], [1, 2]]], [37, [[2, 3], [1, 2]]], [41, [[8, 1]]], [43, [[2, 3], [1, 2]]], [47, [[2, 3], [1, 2]]], [53, [[3, 2], [1, 2]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24], 'galois_label': '8T23', 'galt': 23, 'grd': 25.357444666211933, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.265847707.1', 'local_algs': ['m643.1.2.0', 'm643.2.1.1', 'm643.2.2.2'], 'monogenic': 0, 'num_ram': 1, 'r2': 3, 'ramps': [643], 'rd': 11.3000174684, 'regulator': {'__RealLiteral__': 0, 'data': '10.712578457', 'prec': 40}, 'res': {'ae': ['-1,9,-6,2,-3,5,-1,-1,1'], 'sib': ['1,4,38,99,304,446,920,467,50,-564,65,117,-51,7,7,-2,1', '5,-29,25,-37,227,-426,697,-1100,1364,-1116,766,-156,-504,636,-212,-121,171,-86,9,23,-10,-8,11,-5,1']}, 'subfield_mults': [1], 'subfields': ['1.-2.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{74}{127} a^{7} - \\frac{147}{127} a^{6} + \\frac{208}{127} a^{5} + \\frac{118}{127} a^{4} - \\frac{537}{127} a^{3} + \\frac{1299}{127} a^{2} - \\frac{728}{127} a + \\frac{142}{127} \\)', '\\( \\frac{61}{127} a^{7} - \\frac{92}{127} a^{6} + \\frac{144}{127} a^{5} + \\frac{111}{127} a^{4} - \\frac{362}{127} a^{3} + \\frac{997}{127} a^{2} - \\frac{377}{127} a + \\frac{69}{127} \\)', '\\( \\frac{61}{127} a^{7} - \\frac{92}{127} a^{6} + \\frac{144}{127} a^{5} + \\frac{111}{127} a^{4} - \\frac{362}{127} a^{3} + \\frac{870}{127} a^{2} - \\frac{377}{127} a + \\frac{69}{127} \\)', '\\( \\frac{36}{127} a^{7} - \\frac{123}{127} a^{6} + \\frac{187}{127} a^{5} - \\frac{49}{127} a^{4} - \\frac{426}{127} a^{3} + \\frac{1061}{127} a^{2} - \\frac{1226}{127} a + \\frac{378}{127} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/127*a^7 - 14/127*a^6 + 44/127*a^5 - 19/127*a^4 - 33/127*a^3 + 33/127*a^2 - 27/127*a - 53/127']}