Number field data - 8.0.1334161125.1

Formats: - HTML - YAML - JSON - 2024-05-20T08:52:35.264999

• 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': [2], 'class_number': 2, 'cm': False, 'coeffs': [3, -9, 15, -6, 10, -7, 3, -1, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 1334161125, 'disc_rad': 165, 'disc_sign': 1, 'frobs': [[2, [[8, 1]]], [3, [0]], [5, [0]], [7, [[8, 1]]], [11, [0]], [13, [[8, 1]]], [17, [[8, 1]]], [19, [[2, 4]]], [23, [[2, 3], [1, 2]]], [29, [[2, 4]]], [31, [[4, 2]]], [37, [[2, 3], [1, 2]]], [41, [[2, 4]]], [43, [[8, 1]]], [47, [[2, 3], [1, 2]]], [53, [[2, 3], [1, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 8, 8], 'galois_label': '8T6', 'galt': 6, 'grd': 16.90527678711191, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.0.1334161125.1', 'local_algs': ['3.4.3.1', '3.4.3.2', '5.2.1.2', '5.2.0.1', '5.4.2.1', '11.2.1.2', '11.2.1.2', '11.2.1.2', '11.2.1.2'], 'minimal_sibling': [1, 13, 11, -11, -2, 8, -1, -1, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [3, 5, 11], 'rd': 13.824551008, 'regulator': {'__RealLiteral__': 0, 'data': '17.0595109709', 'prec': 44}, 'res': {'gal': ['1,-7,26,-62,86,-71,78,-126,175,-126,78,-71,86,-62,26,-7,1'], 'sib': ['1,13,11,-11,-2,8,-1,-1,1', '1,-7,26,-62,86,-71,78,-126,175,-126,78,-71,86,-62,26,-7,1']}, 'subfield_mults': [1, 1], 'subfields': ['3.-1.1', '3.-6.4.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{5}{33} a^{7} - \\frac{4}{33} a^{6} + \\frac{23}{33} a^{5} - \\frac{16}{11} a^{4} + \\frac{23}{11} a^{3} - \\frac{23}{11} a^{2} + \\frac{49}{11} a - \\frac{14}{11} \\)', '\\( \\frac{1}{33} a^{7} - \\frac{1}{11} a^{6} + \\frac{3}{11} a^{5} - \\frac{25}{33} a^{4} + \\frac{9}{11} a^{3} - \\frac{20}{11} a^{2} + \\frac{23}{11} a - \\frac{5}{11} \\)', '\\( \\frac{1}{33} a^{7} - \\frac{1}{11} a^{6} + \\frac{3}{11} a^{5} - \\frac{25}{33} a^{4} + \\frac{9}{11} a^{3} - \\frac{9}{11} a^{2} + \\frac{12}{11} a - \\frac{5}{11} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 + 1/3*a^5 + 1/3*a^4', '1/33*a^7 - 1/11*a^6 + 3/11*a^5 + 8/33*a^4 - 2/11*a^3 + 2/11*a^2 + 1/11*a - 5/11']}