Artin representation data - 4.2485125.6t10.d

Formats: - HTML - YAML - JSON - 2024-04-30T23:44:38.593353

• artin_reps •

  Column	Type
  BadPrimes	jsonb
  Baselabel	text
  CharacterField	smallint
  Conductor	numeric
  Container	text
  Dets	text[]
  Dim	smallint
  GalConjSigns	jsonb
  Galn	smallint
  GaloisConjugates	jsonb
  GaloisConjugatesSigns	integer[]
  GaloisLabel	text
  Galt	integer
  HardPrimes	jsonb
  Hide	smallint
  Indicator	smallint
  Is_Even	boolean
  NFGal	jsonb
  NumBadPrimes	smallint
  Proj_GAP	integer[]
  Proj_Polynomial	numeric[]
  Proj_nTj	integer[]

  
  {'BadPrimes': [3, 5, 47], 'Baselabel': '4.2485125.6t10.d', 'CharacterField': 1, 'Conductor': 2485125, 'Container': '6t10', 'Dets': ['1.5.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [0], [-2], [1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [5, 7, 8, 5, 7], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [0], [-2], [0], [1]], [[1], [2], [3], [2], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [0], [-1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T10', 'Galt': 10, 'HardPrimes': [2, 3, 5, 17, 47], 'Hide': 1, 'Indicator': 1, 'Is_Even': True, 'NFGal': [1, 12, 9, -9, 9, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [36, 9], 'Proj_Polynomial': [1, 12, 9, -9, 9, -3, 1], 'Proj_nTj': [6, 10]}
• artin_field_data •

  Column	Type
  ArtinReps	jsonb
  ComplexConjugation	smallint
  ConjClasses	jsonb
  FrobResolvents	jsonb
  Frobs	jsonb
  G-Gens	jsonb
  G-Name	text
  Polynomial	jsonb
  QpRts	jsonb
  QpRts-minpoly	jsonb
  QpRts-p	integer
  QpRts-prec	integer
  Size	numeric
  TransitiveDegree	smallint

  
  {'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.705.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.705.4t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '4.2485125.6t10.c', 'Character': [[4], [0], [1], [-2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.2485125.6t10.d', 'Character': [[4], [0], [-2], [1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '9', 'Order': 2, 'Representative': [4, 3, 2, 1, 5, 6]}, {'Size': '4', 'Order': 3, 'Representative': [1, 3, 6, 4, 5, 2]}, {'Size': '4', 'Order': 3, 'Representative': [4, 3, 6, 5, 1, 2]}, {'Size': '9', 'Order': 4, 'Representative': [2, 4, 1, 3, 6, 5]}, {'Size': '9', 'Order': 4, 'Representative': [3, 1, 4, 2, 6, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['3388081932', '9864304659', '1856591928', '134454816', '1782432', '-195399', '-288', '1179', '63', '1'], 'ConjugacyClass': 5}, {'RootOf': ['256215312', '-153454176', '82910628', '-6784884', '1116207', '71091', '6057', '1179', '63', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [3, 3]}], 'Frobs': [6, 6, 1, 5, 4, 5, 6, 3, 6, 2, 2, 5, 3, 5, 5, 5, 4, 3, 6, 2, 5, 2, 5, 3, 5, 2, 6, 5, 4, 6, 6, 2, 5, 4, 4, 2, 5, 5, 5, 5, 2, 2, 2, 5, 6, 4, 2, 5, 5, 1, 6, 3, 4, 2, 5, 5, 4, 3, 5, 3, 6, 6, 5, 3, 5, 5, 4, 5, 6, 4, 5, 2, 6, 5, 2, 5, 2, 5, 2, 3, 2, 2, 2, 5, 2, 6, 2, 5, 3, 5, 5, 3, 5, 2, 3, 6, 2, 2, 6, 4, 6, 5, 6, 2, 3, 6, 5, 6, 2, 3, 6, 6, 6, 2, 2, 3, 6, 6, 5, 3, 4, 5, 5, 5, 2, 4, 2, 3, 6, 6, 2, 6, 2, 6, 2, 2, 5, 6, 5, 2, 4, 3, 6, 6, 3, 2, 6, 5, 3, 5, 6, 4, 6, 5, 5, 2, 1, 3, 6, 2, 6, 6, 5, 4, 6, 6, 3, 6], 'G-Gens': [[2, 4, 1, 3, 6, 5], [4, 2, 3, 5, 1, 6], [1, 3, 6, 4, 5, 2]], 'G-Name': 'C3^2:C4', 'Polynomial': [1, 12, 9, -9, 9, -3, 1], 'QpRts': [['2599422009305964272', '0'], ['3724473814078612215', '-897318346414948473'], ['4738856702120171189', '897318346414948473'], ['-3918215206347346101', '4393151357322374913'], ['3513068060460280066', '-4393151357322374913'], ['-396976666659079449', '0']], 'QpRts-minpoly': [2, 24, 1], 'QpRts-p': 29, 'QpRts-prec': 13, 'Size': 36, 'TransitiveDegree': 6}