Number field data - 6.0.108222553539.1

Formats: - HTML - YAML - JSON - 2025-12-04T20:15:58.604010

• 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, 4], 'class_number': 8, 'cm': False, 'coeffs': [3007, -435, 456, -43, 24, -3, 1], 'conductor': 0, 'degree': 6, 'dirichlet_group': [], 'disc_abs': 108222553539, 'disc_rad': 6873, 'disc_sign': -1, 'frobs': [[2, [[2, 3]]], [3, [0]], [5, [[3, 2]]], [7, [[4, 1], [1, 2]]], [11, [[4, 1], [1, 2]]], [13, [[3, 2]]], [17, [[3, 2]]], [19, [[4, 1], [1, 2]]], [23, [[3, 2]]], [29, [0]], [31, [[4, 1], [1, 2]]], [37, [[3, 2]]], [41, [[3, 2]]], [43, [[3, 2]]], [47, [[3, 2]]], [53, [[4, 1], [1, 2]]], [59, [[4, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 12, 12], 'galois_label': '6T8', 'galt': 8, 'grd': 82.90355842785037, 'index': 4, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '6.0.108222553539.1', 'local_algs': ['3.2.1.0a1.1', '3.1.2.1a1.2', '3.1.2.1a1.1', '29.1.2.1a1.2', '29.2.2.2a1.2', '79.1.2.1a1.2', '79.2.2.2a1.2'], 'minimal_sibling': [4, -3, -4, 0, 1], 'monogenic': -1, 'narrow_class_group': [2, 4], 'narrow_class_number': 8, 'num_ram': 3, 'r2': 3, 'ramps': [3, 29, 79], 'rd': 69.0323984707, 'regulator': {'__RealLiteral__': 0, 'data': '578.56057074', 'prec': 40}, 'res': {'gal': ['6098539,-21886824,31030032,-7877106,-7146464,-530184,21689046,-9266592,-3795928,2049342,1740264,-104688,-559052,-74184,102912,27450,-880,-4488,-1782,336,328,-6,-24,0,1'], 'sex': ['0,1', '0,1', '4,-3,-4,0,1'], 'sib': ['4,-3,-4,0,1', '-72,0,72,219,292,48,-9,-12,32,-3,0,0,1', '-8,0,-4,-3,2,0,1', '2401,0,3284,0,2620,0,1102,0,220,0,20,0,1', '90844,-4770,17041,-576,1554,-18,64,0,1']}, 'subfield_mults': [1], 'subfields': ['-3.8.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{229}{36} a^{5} + \\frac{41}{6} a^{4} + \\frac{3521}{36} a^{3} - \\frac{1085}{9} a^{2} + \\frac{2691}{4} a - \\frac{15733}{9} \\)', '\\( \\frac{47}{36} a^{4} - \\frac{47}{18} a^{3} + \\frac{1387}{12} a^{2} - \\frac{2057}{18} a + \\frac{33911}{36} \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/6*a^2 - 1/6*a + 1/6', '1/6*a^3 + 1/6', '1/36*a^4 - 1/18*a^3 - 1/12*a^2 + 1/9*a - 5/36', '1/108*a^5 - 1/108*a^4 - 5/108*a^3 + 1/108*a^2 - 1/108*a - 5/108']}