Number field data - 8.6.307235186944.2

Formats: - HTML - YAML - JSON - 2026-03-03T01:14:19.211625

• 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
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [2, 2, -26, 26, 8, -6, -3, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 307235186944, 'disc_rad': 1414, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[8, 1]]], [5, [[6, 1], [2, 1]]], [7, [0]], [11, [[8, 1]]], [13, [[6, 1], [2, 1]]], [17, [[6, 1], [2, 1]]], [19, [[6, 1], [1, 2]]], [23, [[3, 2], [2, 1]]], [29, [[4, 2]]], [31, [[3, 2], [2, 1]]], [37, [[2, 4]]], [41, [[4, 2]]], [43, [[4, 1], [2, 2]]], [47, [[3, 2], [2, 1]]], [53, [[2, 4]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [608, 288, 192], 'galois_label': '8T44', 'galt': 44, 'grd': 129.60299666924007, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '8.6.307235186944.2', 'local_algs': ['2.1.2.2a1.2', '2.1.6.6a1.1', '7.2.4.6a1.1', '101.2.1.0a1.1', '101.2.1.0a1.1', '101.2.2.2a1.2'], 'minimal_sibling': [-73, -181, -194, -67, 32, 1, -6, -1, 1], 'monogenic': 0, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 1, 'ramps': [2, 7, 101], 'rd': 27.285622676, 'regulator': {'__RealLiteral__': 0, 'data': '2009.20325773', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['8.1.-7.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{46}{127} a^{7} - \\frac{49}{127} a^{6} - \\frac{170}{127} a^{5} - \\frac{457}{127} a^{4} - \\frac{73}{127} a^{3} + \\frac{998}{127} a^{2} - \\frac{241}{127} a - \\frac{125}{127} \\)', '\\( \\frac{199}{127} a^{7} - \\frac{281}{127} a^{6} - \\frac{752}{127} a^{5} - \\frac{1654}{127} a^{4} + \\frac{587}{127} a^{3} + \\frac{5477}{127} a^{2} - \\frac{1846}{127} a - \\frac{411}{127} \\)', '\\( \\frac{117}{127} a^{7} - \\frac{155}{127} a^{6} - \\frac{460}{127} a^{5} - \\frac{1005}{127} a^{4} + \\frac{303}{127} a^{3} + \\frac{3201}{127} a^{2} - \\frac{1063}{127} a - \\frac{271}{127} \\)', '\\( \\frac{82}{127} a^{7} - \\frac{126}{127} a^{6} - \\frac{292}{127} a^{5} - \\frac{649}{127} a^{4} + \\frac{284}{127} a^{3} + \\frac{2276}{127} a^{2} - \\frac{1037}{127} a - \\frac{267}{127} \\)', '\\( \\frac{47}{127} a^{7} - \\frac{97}{127} a^{6} - \\frac{124}{127} a^{5} - \\frac{293}{127} a^{4} + \\frac{392}{127} a^{3} + \\frac{1097}{127} a^{2} - \\frac{1138}{127} a + \\frac{245}{127} \\)', '\\( \\frac{199}{127} a^{7} - \\frac{281}{127} a^{6} - \\frac{752}{127} a^{5} - \\frac{1654}{127} a^{4} + \\frac{587}{127} a^{3} + \\frac{5477}{127} a^{2} - \\frac{1846}{127} a - \\frac{665}{127} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/127*a^7 - 48/127*a^6 + 46/127*a^5 + 37/127*a^4 - 43/127*a^3 - 28/127*a^2 - 8/127*a - 11/127']}
• nf_fields_extra •

  Column	Type
  dirichlet_group	bigint[]
  frobs	jsonb
  label	text
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [[8, 1]]], [5, [[6, 1], [2, 1]]], [7, [0]], [11, [[8, 1]]], [13, [[6, 1], [2, 1]]], [17, [[6, 1], [2, 1]]], [19, [[6, 1], [1, 2]]], [23, [[3, 2], [2, 1]]], [29, [[4, 2]]], [31, [[3, 2], [2, 1]]], [37, [[2, 4]]], [41, [[4, 2]]], [43, [[4, 1], [2, 2]]], [47, [[3, 2], [2, 1]]], [53, [[2, 4]]], [59, [[8, 1]]]], 'label': '8.6.307235186944.2', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{46}{127} a^{7} - \\frac{49}{127} a^{6} - \\frac{170}{127} a^{5} - \\frac{457}{127} a^{4} - \\frac{73}{127} a^{3} + \\frac{998}{127} a^{2} - \\frac{241}{127} a - \\frac{125}{127} \\)', '\\( \\frac{199}{127} a^{7} - \\frac{281}{127} a^{6} - \\frac{752}{127} a^{5} - \\frac{1654}{127} a^{4} + \\frac{587}{127} a^{3} + \\frac{5477}{127} a^{2} - \\frac{1846}{127} a - \\frac{411}{127} \\)', '\\( \\frac{117}{127} a^{7} - \\frac{155}{127} a^{6} - \\frac{460}{127} a^{5} - \\frac{1005}{127} a^{4} + \\frac{303}{127} a^{3} + \\frac{3201}{127} a^{2} - \\frac{1063}{127} a - \\frac{271}{127} \\)', '\\( \\frac{82}{127} a^{7} - \\frac{126}{127} a^{6} - \\frac{292}{127} a^{5} - \\frac{649}{127} a^{4} + \\frac{284}{127} a^{3} + \\frac{2276}{127} a^{2} - \\frac{1037}{127} a - \\frac{267}{127} \\)', '\\( \\frac{47}{127} a^{7} - \\frac{97}{127} a^{6} - \\frac{124}{127} a^{5} - \\frac{293}{127} a^{4} + \\frac{392}{127} a^{3} + \\frac{1097}{127} a^{2} - \\frac{1138}{127} a + \\frac{245}{127} \\)', '\\( \\frac{199}{127} a^{7} - \\frac{281}{127} a^{6} - \\frac{752}{127} a^{5} - \\frac{1654}{127} a^{4} + \\frac{587}{127} a^{3} + \\frac{5477}{127} a^{2} - \\frac{1846}{127} a - \\frac{665}{127} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/127*a^7 - 48/127*a^6 + 46/127*a^5 + 37/127*a^4 - 43/127*a^3 - 28/127*a^2 - 8/127*a - 11/127']}