Number field data - 8.2.139968000000.2

Formats: - HTML - YAML - JSON - 2025-09-01T06:28:03.908490

• 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': [-300, 0, 60, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 139968000000, 'disc_rad': 30, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[3, 2], [1, 2]]], [11, [[8, 1]]], [13, [[3, 2], [1, 2]]], [17, [[8, 1]]], [19, [[3, 2], [1, 2]]], [23, [[8, 1]]], [29, [[8, 1]]], [31, [[3, 2], [1, 2]]], [37, [[4, 2]]], [41, [[2, 3], [1, 2]]], [43, [[6, 1], [2, 1]]], [47, [[8, 1]]], [53, [[2, 3], [1, 2]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [76, 42, 40], 'galois_label': '8T23', 'galt': 23, 'grd': 29.963112711597162, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '8.2.139968000000.2', 'local_algs': ['2.1.8.12b1.2', '3.1.8.7a1.2', '5.1.2.1a1.1', '5.1.6.5a1.2'], 'monogenic': 0, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 5], 'rd': 24.7316786358, 'regulator': {'__RealLiteral__': 0, 'data': '486.909901635', 'prec': 44}, 'res': {'ae': ['-5,-10,10,-40,40,-10,4,-4,1'], 'sib': ['-2744,1568,-2968,-3536,-1176,-2472,-1976,2576,-4828,4112,-3688,2216,-1276,1088,128,-376,122,-412,226,-84,84,-38,8,-4,1', '25,50,150,-500,-100,450,1060,-1420,1245,-130,-200,240,-64,4,12,-4,1']}, 'subfield_mults': [1], 'subfields': ['4.-8.0.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3}{820} a^{7} + \\frac{5}{164} a^{6} + \\frac{1}{41} a^{5} + \\frac{3}{82} a^{4} - \\frac{7}{41} a^{3} - \\frac{21}{82} a^{2} - \\frac{24}{41} a + \\frac{46}{41} \\)', '\\( \\frac{1}{82} a^{6} - \\frac{7}{82} a^{4} + \\frac{4}{41} a^{2} + \\frac{2}{41} \\)', '\\( \\frac{1}{41} a^{6} - \\frac{7}{41} a^{4} - \\frac{33}{41} a^{2} + \\frac{127}{41} \\)', '\\( \\frac{17}{410} a^{7} - \\frac{59}{820} a^{6} + \\frac{9}{82} a^{5} - \\frac{6}{41} a^{4} + \\frac{19}{82} a^{3} - \\frac{39}{82} a^{2} + \\frac{138}{41} a - \\frac{266}{41} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4', '1/4*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a', '1/820*a^6 - 13/82*a^4 - 1/2*a^3 + 9/82*a^2 - 8/41', '1/820*a^7 + 15/164*a^5 - 16/41*a^3 - 1/2*a^2 + 25/82*a']}