Number field data - 5.1.9828125.1

Formats: - HTML - YAML - JSON - 2026-03-24T11:08:55.112069

• 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': [-13, -5, 0, 0, 0, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 9828125, 'disc_rad': 3145, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [156, 60, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 203.229303310938, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.1.9828125.1', 'local_algs': ['5.1.5.6a1.1', '17.1.2.1a1.2', '17.3.1.0a1.1', '37.1.1.0a1.1', '37.2.1.0a1.1', '37.1.2.1a1.1'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 2, 'ramps': [5, 17, 37], 'rd': 25.0319183932, 'regulator': {'__RealLiteral__': 0, 'data': '46.1056422217', 'prec': 44}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 1, '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, [[3, 1], [2, 1]]], [3, [[3, 1], [2, 1]]], [5, [0]], [7, [[4, 1], [1, 1]]], [11, [[4, 1], [1, 1]]], [13, [[4, 1], [1, 1]]], [17, [0]], [19, [[4, 1], [1, 1]]], [23, [[5, 1]]], [29, [[3, 1], [1, 2]]], [31, [[2, 2], [1, 1]]], [37, [0]], [41, [[3, 1], [2, 1]]], [43, [[4, 1], [1, 1]]], [47, [[5, 1]]], [53, [[5, 1]]], [59, [[4, 1], [1, 1]]]], 'label': '5.1.9828125.1', 'res': {'sib': ['-147095,-811050,-301735,-460920,-216560,70778,70175,11780,-2635,-330,41,-60,-100,-15,0,1', '-169,-260,-100,0,0,-143,15,0,0,0,1', '-28130000,-3102500,4094625,-148150,-42125,-19638,3095,-325,100,0,1', '1,-716,-780,-360,-70,-1,1', '108097344,-229810560,212656960,-79865880,-3107880,14340568,-4076275,1497680,-433555,466885,-362387,143525,12565,-19415,8530,-2836,1090,-250,55,-5,1', '111890672965,59503738480,81454852080,100608711115,76031130155,40439184830,15048663605,1459653910,-940669600,-645205300,157016606,107523392,49545957,-2506794,-2737741,-1520014,-82883,53322,31881,3129,174,-172,-32,-1,1', '1212317,-182523,290228,-199520,60400,46226,-13779,-1306,220,60,-1,-6,1', '21744223936,46304068840,51915988275,34814852465,13798560275,1533611546,-1590846500,-1040206240,-257277985,5599570,24229383,7660270,1524865,400690,140135,28924,1590,-545,-110,0,1', '493775,-451500,1334725,-1101275,1948350,-1236160,1032125,-482520,402180,-298425,-27064,59855,2840,-6430,-1185,1397,-345,-15,40,-10,1', '567801102259,27069378387175,-213874220438460,148530331228630,35136262507235,-53152564497841,24762030461235,1803210164570,-7128228041590,682274990480,479246645496,-448396416835,5941217430,68329411240,-20863077960,-2917535813,1843492955,-249705705,-338047100,92497305,8925833,-6770990,-1306515,507865,-1225,-8682,-890,265,25,-10,1', '75053314565,-99512023725,-74142401880,83094974620,67407073895,-18866942014,-46391156890,-8568780925,16761096610,9172206685,-2372658116,-4169805800,-242566635,1111251435,201064080,-196480188,-62094665,32718140,9707095,-4493760,-855914,307460,131730,-31670,-9555,1363,720,-40,-35,0,1', '846053678328350225,-2242683455009773500,3301028918258587500,-3424762629649361250,3001502911892330475,-2263607897802404850,1575806054803947825,-1024063478804862650,622848916520022700,-351107894145665950,185888757961622955,-91426546828736200,42091414261327400,-18545649837597850,7809803608164990,-3078228294918830,1087253837703205,-344314352180210,106496403688645,-33747506029130,9546154193421,-1594566086340,-196131903605,212398097010,-58688453155,6264346964,247551085,166802360,-148868530,17837880,12478496,-7793390,2703670,-635810,145080,-33636,6305,-1010,135,-10,1', '941640791,320277635665,-6396792226235,42622028669345,-113113033981280,121833888071623,-31233170822050,-16527938473410,17954411089175,4780937409995,-5892096788442,2169754180915,249956662405,-250152127525,40407933825,32687509341,-17258571980,4912183500,-752437555,114290275,-18142252,3674370,167630,-128965,32015,-4622,1910,-260,30,0,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{3} a^{4} - \\frac{1}{3} a^{3} + \\frac{1}{3} a^{2} - \\frac{1}{3} a - \\frac{7}{3} \\)', '\\( \\frac{53}{3} a^{4} - \\frac{2}{3} a^{3} - \\frac{100}{3} a^{2} + \\frac{289}{3} a - \\frac{743}{3} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 - 1/3*a^3 + 1/3*a^2 - 1/3*a - 1/3']}