Number field data - 8.4.56953125.1

Formats: - HTML - YAML - JSON - 2026-03-16T21:39:04.903628

• 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
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 1, -13, 13, -5, 2, 2, -1, 1], 'conductor': 0, 'degree': 8, 'disc_abs': 56953125, 'disc_rad': 15, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 14], 'galois_label': '8T7', 'galt': 7, 'grd': 9.320510388204081, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.4.56953125.1', 'local_algs': ['3.2.4.6a1.1', '5.1.8.7a1.4'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 2, 'ramps': [3, 5], 'rd': 9.3205103882, 'regulator': {'__RealLiteral__': 0, 'data': '5.73476282291', 'prec': 44}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.4.-4.-1.1'], 'torsion_order': 2, 'unit_signature_rank': 3, 'used_grh': False}
• 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, [[8, 1]]], [3, [0]], [5, [0]], [7, [[8, 1]]], [11, [[4, 2]]], [13, [[8, 1]]], [17, [[8, 1]]], [19, [[4, 2]]], [23, [[8, 1]]], [29, [[2, 2], [1, 4]]], [31, [[2, 4]]], [37, [[8, 1]]], [41, [[4, 2]]], [43, [[8, 1]]], [47, [[8, 1]]], [53, [[8, 1]]], [59, [[2, 2], [1, 4]]]], 'label': '8.4.56953125.1', 'res': {'gal': ['1,-5,16,-30,57,-110,183,-240,250,-215,157,-100,57,-30,14,-5,1'], 'sib': ['1,-5,16,-30,57,-110,183,-240,250,-215,157,-100,57,-30,14,-5,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{47}{571} a^{7} - \\frac{7}{571} a^{6} + \\frac{3}{571} a^{5} + \\frac{133}{571} a^{4} - \\frac{219}{571} a^{3} + \\frac{48}{571} a^{2} + \\frac{13}{571} a - \\frac{355}{571} \\)', '\\( \\frac{355}{571} a^{7} - \\frac{308}{571} a^{6} + \\frac{703}{571} a^{5} + \\frac{713}{571} a^{4} - \\frac{1642}{571} a^{3} + \\frac{4396}{571} a^{2} - \\frac{4567}{571} a + \\frac{368}{571} \\)', '\\( \\frac{366}{571} a^{7} - \\frac{176}{571} a^{6} + \\frac{728}{571} a^{5} + \\frac{1060}{571} a^{4} - \\frac{1183}{571} a^{3} + \\frac{4225}{571} a^{2} - \\frac{2936}{571} a - \\frac{116}{571} \\)', '\\( \\frac{51}{571} a^{7} + \\frac{41}{571} a^{6} + \\frac{64}{571} a^{5} + \\frac{363}{571} a^{4} - \\frac{104}{571} a^{3} + \\frac{453}{571} a^{2} + \\frac{658}{571} a - \\frac{531}{571} \\)', '\\( \\frac{132}{571} a^{7} - \\frac{129}{571} a^{6} + \\frac{300}{571} a^{5} + \\frac{167}{571} a^{4} - \\frac{773}{571} a^{3} + \\frac{1945}{571} a^{2} - \\frac{2126}{571} a - \\frac{98}{571} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/571*a^7 + 12/571*a^6 + 158/571*a^5 - 228/571*a^4 - 114/571*a^3 + 244/571*a^2 - 267/571*a - 44/571']}