Number field data - 8.0.8704143616.1

Formats: - HTML - YAML - JSON - 2023-12-08T07:11:51.460403

• 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_label	text
  galt	integer
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  minimal_sibling	integer[]
  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': [2], 'class_number': 2, 'cm': False, 'coeffs': [64, -128, 100, 4, -43, 18, 2, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 8704143616, 'disc_rad': 238, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 2]]], [5, [[4, 2]]], [7, [0]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [0]], [19, [[2, 4]]], [23, [[4, 2]]], [29, [[2, 2], [1, 4]]], [31, [[4, 2]]], [37, [[2, 2], [1, 4]]], [41, [[4, 2]]], [43, [[2, 4]]], [47, [[2, 4]]], [53, [[1, 8]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_label': '8T11', 'galt': 11, 'inessentialp': [2], 'is_galois': False, 'iso_number': 1, 'label': '8.0.8704143616.1', 'local_algs': ['2.2.2.1', '2.2.2.1', '2.2.2.1', '2.2.2.1', '7.8.6.1', '17.4.2.2', '17.4.0.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 4, 'ramps': [2, 7, 17], 'rd': 17.4769545176, 'regulator': {'__RealLiteral__': 0, 'data': '370.649114462', 'prec': 44}, 'res': {'gal': ['16384,0,33856,0,34400,0,15636,0,1972,0,-67,0,43,0,-17,0,1'], 'sib': ['106,450,-13,-30,-119,30,1,-2,1', '128,-328,288,-74,0,-19,9,-1,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-7.0.1', '1.0.1', '2.-1.1', '4.0.-3.0.1'], 'torsion_gen': '\\( \\frac{17}{608} a^{7} - \\frac{7}{152} a^{6} + \\frac{21}{304} a^{5} + \\frac{147}{304} a^{4} - \\frac{511}{608} a^{3} - \\frac{7}{304} a^{2} + \\frac{175}{76} a - \\frac{33}{19} \\)', 'torsion_order': 4, 'units': ['\\( \\frac{65}{608} a^{7} - \\frac{5}{76} a^{6} + \\frac{49}{304} a^{5} + \\frac{571}{304} a^{4} - \\frac{863}{608} a^{3} - \\frac{713}{304} a^{2} + \\frac{201}{38} a - \\frac{58}{19} \\)', '\\( \\frac{3}{304} a^{7} - \\frac{17}{152} a^{6} + \\frac{35}{152} a^{5} - \\frac{21}{152} a^{4} - \\frac{193}{304} a^{3} + \\frac{43}{38} a^{2} - \\frac{69}{76} a + \\frac{4}{19} \\)', '\\( \\frac{67}{304} a^{7} + \\frac{4}{19} a^{6} + \\frac{47}{152} a^{5} + \\frac{709}{152} a^{4} + \\frac{1035}{304} a^{3} - \\frac{763}{152} a^{2} + \\frac{85}{19} a + \\frac{83}{19} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a', '1/2*a^4 - 1/2*a^2', '1/4*a^5 - 1/4*a^4 - 1/4*a^3 - 1/4*a^2 - 1/2*a', '1/8*a^6 - 1/4*a^4 - 1/4*a^3 - 3/8*a^2 - 1/4*a', '1/608*a^7 - 3/76*a^6 + 37/304*a^5 + 31/304*a^4 - 39/608*a^3 + 51/304*a^2 + 9/19*a + 7/19']}