Artin representation data - 4.1516563.12t34.b

Formats: - HTML - YAML - JSON - 2025-03-21T00:49:23.500541

• 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, 79], 'Baselabel': '4.1516563.12t34.b', 'CharacterField': 1, 'Conductor': 1516563, 'Container': '12t34', 'Dets': ['1.3.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [-2], [0], [0], [-2], [1], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [10, 11], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [2], [0], [-2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [0], [-2], [0], [1]], [[1], [2], [3], [2], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [0], [0], [-1]], [[1], [-1], [0], [1], [-1]], [[1], [0], [1], [0], [1]], [[1]], [[1], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T13', 'Galt': 13, 'HardPrimes': [3, 79], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, 0, 3, -1, -3, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [72, 40], 'Proj_Polynomial': [1, 0, 3, -1, -3, 0, 1], 'Proj_nTj': [6, 13]}
• 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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.79.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.237.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.711.4t3.a', 'Character': [[2], [0], [0], [-2], [2], [2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.19197.6t13.b', 'Character': [[4], [0], [2], [0], [1], [-2], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.119808477.12t34.b', 'Character': [[4], [0], [-2], [0], [1], [-2], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1516563.6t13.b', 'Character': [[4], [2], [0], [0], [-2], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.1516563.12t34.b', 'Character': [[4], [-2], [0], [0], [-2], [1], [0], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '6', 'Order': 2, 'Representative': [3, 4, 1, 2, 6, 5]}, {'Size': '6', 'Order': 2, 'Representative': [1, 5, 3, 4, 2, 6]}, {'Size': '9', 'Order': 2, 'Representative': [1, 5, 3, 6, 2, 4]}, {'Size': '4', 'Order': 3, 'Representative': [2, 5, 3, 4, 1, 6]}, {'Size': '4', 'Order': 3, 'Representative': [2, 5, 4, 6, 1, 3]}, {'Size': '18', 'Order': 4, 'Representative': [3, 6, 1, 2, 4, 5]}, {'Size': '12', 'Order': 6, 'Representative': [4, 6, 1, 2, 3, 5]}, {'Size': '12', 'Order': 6, 'Representative': [1, 5, 4, 6, 2, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 2, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [3, 3]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [6]}], 'Frobs': [7, 3, 7, 9, 7, 6, 8, 6, 7, 8, 4, 3, 8, 9, 8, 8, 2, 9, 4, 8, 5, 3, 7, 7, 4, 7, 9, 8, 9, 8, 9, 7, 8, 3, 2, 5, 9, 4, 7, 8, 7, 4, 8, 9, 2, 9, 3, 4, 8, 3, 2, 7, 5, 2, 7, 7, 7, 9, 4, 7, 4, 2, 9, 8, 5, 7, 9, 5, 7, 9, 8, 2, 4, 9, 9, 7, 7, 4, 8, 3, 2, 6, 7, 4, 4, 2, 8, 4, 8, 9, 7, 7, 4, 2, 6, 2, 8, 2, 5, 4, 6, 7, 7, 7, 5, 9, 8, 7, 7, 3, 3, 9, 7, 3, 9, 7, 6, 2, 7, 8, 9, 9, 7, 7, 3, 8, 9, 7, 6, 4, 3, 7, 5, 4, 7, 3, 7, 4, 8, 7, 6, 7, 9, 8, 9, 7, 3, 7, 9, 7, 6, 8, 9, 7, 1, 7, 5, 8, 9, 7, 2, 7, 5, 7, 8, 2, 9, 5], 'G-Gens': [[3, 4, 1, 2, 6, 5], [2, 1, 3, 4, 5, 6], [2, 5, 3, 4, 1, 6]], 'G-Name': 'S3wrC2', 'Polynomial': [1, 0, 3, -1, -3, 0, 1], 'QpRts': [['-13526389', '0'], ['9073399', '-13661645'], ['-10776607', '0'], ['13078545', '5466422'], ['4452990', '13661645'], ['-2301938', '-5466422']], 'QpRts-minpoly': [3, 29, 1], 'QpRts-p': 31, 'QpRts-prec': 5, 'Size': 72, 'TransitiveDegree': 6}