Number field data - 5.1.70081.1

Formats: - HTML - YAML - JSON - 2024-06-08T22:19:26.867668

• 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[]
  minimal_sibling	numeric[]
  monogenic	smallint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	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': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, 4, 1, -1, 1], 'conductor': 0, 'degree': 5, 'dirichlet_group': [], 'disc_abs': 70081, 'disc_rad': 70081, 'disc_sign': 1, 'frobs': [[2, [[5, 1]]], [3, [[5, 1]]], [5, [[2, 2], [1, 1]]], [7, [[5, 1]]], [11, [0]], [13, [[3, 1], [2, 1]]], [17, [[4, 1], [1, 1]]], [19, [[3, 1], [1, 2]]], [23, [0]], [29, [[2, 1], [1, 3]]], [31, [[4, 1], [1, 1]]], [37, [[3, 1], [1, 2]]], [41, [[4, 1], [1, 1]]], [43, [[4, 1], [1, 1]]], [47, [[2, 2], [1, 1]]], [53, [[3, 1], [1, 2]]], [59, [[5, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60, 60, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 264.7281624610423, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.1.70081.1', 'local_algs': ['11.2.1.2', '11.3.0.1', '23.2.1.2', '23.3.0.1', 'm277.1.1.0', 'm277.1.2.0', 'm277.2.1.1'], 'monogenic': 1, 'num_ram': 3, 'r2': 2, 'ramps': [11, 23, 277], 'rd': 9.31365310115, 'regulator': {'__RealLiteral__': 0, 'data': '2.28412054249', 'prec': 44}, 'res': {'sib': ['-180207128719925,-585380971359961,-619666269435804,-280740308293840,-71318808519015,-12341383578778,-2051286071030,-371511887147,-81574332986,-15466657130,-1697979251,-89989042,-38994636,-2400166,-474013,-43686,7836,-763,137,-6,1', '-31225,-38155,-5256,12484,9993,-5321,-8402,-5122,-1009,333,379,104,-1,-15,-3,1', '-334375325911,-2865665055,4898591625,-28058070,-62904467,284295,257990,-1905,-506,0,1', '-604915,5471623,-22196662,49696554,-63797922,39715746,7727373,-37695243,36527085,-26631475,23523126,-15088861,-6622721,23089601,-18439265,4154883,2519635,-1263071,-369458,235287,88748,-47165,-19705,10386,2356,-1544,-195,197,-18,-6,1', '-66228,-19175,12649,-1059,18,-1,1', '1,4,0,-9,14,-5,-11,-14,-5,-1,1', '192654071435948725,602408033165895965,843903649496487368,730404191514782946,446852720504100605,207153146331153102,77776208958872859,26139435136198680,8579937423925670,2740642538708932,813483637023285,223488803917615,58220746665988,14493206797987,3455692294010,796535204578,174329445459,36364726476,7288110253,1320000404,236269947,44500860,7242254,891129,169072,25264,2189,161,97,-6,1', '226957555500390625,0,379743943238046875,0,-6854774746057801250,0,8737447460506767250,0,9512717584953519901,0,3120045207699815016,0,448615402221846411,0,26838061273879282,0,757885612425024,0,158970032198600,0,31122961916253,0,3463267505099,0,204550503798,0,8051436331,0,198108773,0,13934555,0,1963454,0,135093,0,5116,0,104,0,1', '3085810773125,5352769434875,861534860525,-9072656382895,-8286874113723,2697814027861,7964678150765,1341003169906,-3420598887552,-1649565213664,616976851482,631092276277,32260871453,-116013551452,-34320405950,9062550431,6431571300,314506120,-581984849,-133728478,22991416,12749612,411557,-623153,-90503,16062,4383,-174,-102,0,1', '344047561,1121617990,3874449285,3770736820,3267655747,1595967738,825518213,275969019,108853876,22262041,8041685,871590,515570,24915,28714,-1034,1236,-147,67,-8,1', '625,2500,2775,-1000,-2574,1796,7010,5896,2679,18,-1627,-2280,1225,-304,-20,170,-73,2,20,-8,1', '90000,0,-31681,0,13096,0,1320,0,97,0,-30,0,1', '959339893428,113601885453,3246221261025,-308993866143,1600739318143,-57544283104,277560419871,29923239860,19029078217,10090480598,463121256,1275310253,34863982,86823831,15685087,2432173,2275465,-191987,185879,-19806,6915,-514,123,-6,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{4} - a^{3} + a^{2} + 4 a + 1 \\)', '\\( a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4']}