Artin representation data - 4.1492992.6t10.c

Formats: - HTML - YAML - JSON - 2024-04-30T20:09:37.420799

• 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': [2, 3], 'Baselabel': '4.1492992.6t10.c', 'CharacterField': 1, 'Conductor': 1492992, 'Container': '6t10', 'Dets': ['1.8.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [0], [1], [-2], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [7, 8], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [0], [-2], [0], [1]], [[1], [-1], [0], [-1], [1]], [[1], [2], [3], [2], [1]], [[1], [0], [0], [0], [-1]], [[1], [0], [0], [0], [-1]], [[1], [-1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T10', 'Galt': 10, 'HardPrimes': [2, 3], 'Hide': 1, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-4, 12, -9, -4, 6, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [36, 9], 'Proj_Polynomial': [-4, 12, -9, -4, 6, 0, 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': '1.8.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.48.4t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.48.4t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '4.1492992.6t10.c', 'Character': [[4], [0], [1], [-2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1492992.6t10.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, 5, 4, 2, 6]}, {'Size': '4', 'Order': 3, 'Representative': [4, 3, 5, 6, 2, 1]}, {'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': ['969348384', '-233834040', '17006112', '1889568', '-393660', '10935', '2916', '-162', '0', '1'], 'ConjugacyClass': 5}, {'RootOf': ['52278048', '-14644152', '1889568', '349920', '-113724', '10935', '324', '-162', '0', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [3, 3]}], 'Frobs': [1, 6, 5, 2, 5, 5, 2, 5, 3, 6, 4, 6, 4, 6, 2, 5, 5, 5, 5, 4, 2, 3, 6, 3, 3, 5, 2, 5, 5, 2, 3, 6, 3, 6, 5, 2, 5, 5, 4, 6, 6, 6, 2, 4, 5, 2, 5, 4, 6, 6, 4, 2, 4, 5, 2, 3, 6, 3, 6, 4, 6, 5, 5, 4, 2, 6, 6, 4, 5, 5, 2, 4, 3, 6, 6, 2, 5, 5, 2, 2, 6, 6, 2, 3, 2, 5, 2, 2, 6, 4, 6, 2, 2, 5, 5, 4, 6, 3, 6, 5, 5, 6, 6, 3, 6, 3, 5, 2, 3, 2, 4, 6, 3, 6, 2, 2, 5, 4, 6, 6, 6, 3, 5, 5, 5, 6, 6, 2, 2, 5, 5, 3, 3, 6, 4, 4, 5, 5, 6, 3, 6, 5, 2, 5, 5, 1, 6, 3, 6, 2, 5, 2, 5, 3, 6, 2, 2, 2, 2, 6, 6, 1, 2, 5, 2, 3, 4, 6], 'G-Gens': [[4, 2, 3, 6, 5, 1], [2, 4, 1, 3, 6, 5], [1, 3, 5, 4, 2, 6]], 'G-Name': 'C3^2:C4', 'Polynomial': [-4, 12, -9, -4, 6, 0, 1], 'QpRts': [['-7552262239757272861', '0'], ['-40359818451136016792', '0'], ['-37598087295449740763', '-19259332173672583053'], ['41288014883042798080', '-19426243975706348517'], ['77957905746585757555', '19259332173672583053'], ['-33735752643285525219', '19426243975706348517']], 'QpRts-minpoly': [3, 6, 1], 'QpRts-p': 7, 'QpRts-prec': 24, 'Size': 36, 'TransitiveDegree': 6}