Number field data - 6.4.4435591023.2

Formats: - HTML - YAML - JSON - 2026-03-24T18:48:31.854343

• 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': [19, 21, 3, -17, -15, 0, 1], 'conductor': 0, 'degree': 6, 'disc_abs': 4435591023, 'disc_rad': 3621, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [86, 36, 36], 'galois_label': '6T13', 'galt': 13, 'grd': 129.0471646971052, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '6.4.4435591023.2', 'local_algs': ['3.1.6.6a1.1', '17.1.1.0a1.1', '17.1.1.0a1.1', '17.2.1.0a1.1', '17.1.2.1a1.1', '71.3.2.3a1.1'], 'minimal_sibling': [33, -15, 33, -9, 9, 0, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 1, 'ramps': [3, 17, 71], 'rd': 40.5345400422, 'regulator': {'__RealLiteral__': 0, 'data': '865.4820841', 'prec': 37}, 'subfield_mults': [1], 'subfields': ['-53.-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, [[4, 1], [2, 1]]], [3, [0]], [5, [[2, 3]]], [7, [[4, 1], [2, 1]]], [11, [[2, 2], [1, 2]]], [13, [[6, 1]]], [17, [0]], [19, [[2, 2], [1, 2]]], [23, [[2, 2], [1, 2]]], [29, [[6, 1]]], [31, [[4, 1], [2, 1]]], [37, [[3, 1], [2, 1], [1, 1]]], [41, [[3, 1], [1, 3]]], [43, [[3, 2]]], [47, [[3, 1], [2, 1], [1, 1]]], [53, [[3, 1], [2, 1], [1, 1]]], [59, [[3, 1], [2, 1], [1, 1]]]], 'label': '6.4.4435591023.2', 'res': {'sex': ['33,-15,33,-9,9,0,1'], 'sib': ['33,-15,33,-9,9,0,1', '-119,153,-75,-135,78,6,-6,0,-3,1', '-18411,0,30219,0,-12252,0,600,0,276,0,-33,0,1', '146047,-238986,249807,-50896,15084,2040,1292,-3312,588,160,-27,-6,1', '185860842001,483388177020,201191574054,754544269812,3442379542458,-198310076934,6029850310974,918079840518,4200598111638,1172467441004,1884850571592,300480370704,487656404901,-4656473046,56046718332,-21517888788,10981964295,-2988903276,2044818510,-320150052,387706401,-46115046,46112616,-13978674,3850146,-973818,476154,-72442,87060,-11280,2886,-1446,141,-36,48,-12,1', '230467,14595,43464,-98626,144,25965,-1713,-3780,585,227,-51,-3,1', '25600,-57600,165696,135216,273180,-36282,-118623,-23445,18930,-5476,2016,4299,306,-816,42,87,0,-6,1', '3454677,185021901,2972287629,-7339781952,3678049944,-2718580725,2531596572,5755750245,-7583156739,11912735934,-17207179137,16407809064,-16996815792,14402325069,-11136092166,8234587872,-5249286108,3235859685,-1754695431,870553944,-408414582,157420134,-59135904,20050740,-3323169,1679274,279495,1035,56898,-18801,5514,-1830,555,-60,39,0,1', '36769588,10641807,44307147,1271442,19735230,-871824,5793000,-164637,1006452,-45516,126447,-5469,10782,-591,636,-3,30,0,1', '3697,-6282,3144,1666,-1797,708,33,-210,141,-32,6,0,1', '42445,77529,22578,-12074,5634,3111,-1758,432,102,-77,30,-6,1', '5516773,-19575642,39378294,-28070414,990732,-34031142,110579447,-118166628,72014196,-31466240,12544284,-8332968,7023757,-4368300,2052336,-749044,233226,-76230,27071,-8712,2442,-550,96,-12,1', '576,24192,120240,51912,16596,133812,23751,31671,8352,-4404,-1764,759,186,-690,-54,105,-6,-6,1', '672341872,2013267168,4272626544,7297323810,11771683437,18007694190,23943456084,28702572132,31225005714,31233235936,28917252657,24254997426,18101316195,11541723300,6482229498,2859713352,1152167967,237041316,77985231,-33448698,19333386,-3336066,12133863,6156,2247543,-653130,143712,-168356,24147,-13368,5991,-744,450,-114,12,-6,1', '73168327,-84266976,336701733,-1487596078,1648703640,-467003616,539391542,318268908,53271438,95026982,25198743,-6819366,6112369,-1912530,-108012,126112,-8253,-15366,12215,-3084,-447,292,-21,-6,1', '9307,23982,33345,33392,26580,9987,2162,69,-180,34,15,-6,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{2}{23} a^{5} - \\frac{5}{23} a^{4} - \\frac{29}{23} a^{3} + \\frac{27}{23} a^{2} + \\frac{42}{23} a + \\frac{52}{23} \\)', '\\( \\frac{25}{23} a^{5} - \\frac{5}{23} a^{4} - \\frac{397}{23} a^{3} - \\frac{318}{23} a^{2} + \\frac{479}{23} a + \\frac{397}{23} \\)', '\\( \\frac{4}{23} a^{5} + \\frac{13}{23} a^{4} - \\frac{58}{23} a^{3} - \\frac{245}{23} a^{2} - \\frac{238}{23} a - \\frac{149}{23} \\)', '\\( \\frac{11}{46} a^{5} + \\frac{7}{46} a^{4} - \\frac{74}{23} a^{3} - \\frac{277}{46} a^{2} - \\frac{149}{23} a - \\frac{197}{46} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/46*a^5 + 9/46*a^4 + 10/23*a^3 - 21/46*a^2 - 1/23*a + 3/46']}