Artin representation data - 2.3700.6t3.e

Formats: - HTML - YAML - JSON - 2025-01-25T19:37:09.837424

• 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, 5, 37], 'Baselabel': '2.3700.6t3.e', 'CharacterField': 1, 'Conductor': 3700, 'Container': '6t3', 'Dets': ['1.148.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [-2], [0], [0], [-1], [1]], 'GalOrbIndex': 1, 'HardFactors': [7, 3, 8, 3, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [-1], [1]], [[1], [1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T3', 'Galt': 3, 'HardPrimes': [2, 3, 5, 7, 37], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-31, -13, 10, 5, 0, -3, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-20, 10, 0, 1], 'Proj_nTj': [3, 2]}
• 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': '1.148.2t1.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': '1.740.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3700.3t2.a', 'Character': [[2], [2], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3700.6t3.e', 'Character': [[2], [-2], [0], [0], [-1], [1]], 'CharacterField': 1}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '1', 'Order': 2, 'Representative': [6, 4, 5, 2, 3, 1]}, {'Size': '3', 'Order': 2, 'Representative': [2, 1, 5, 6, 3, 4]}, {'Size': '3', 'Order': 2, 'Representative': [3, 2, 1, 4, 6, 5]}, {'Size': '2', 'Order': 3, 'Representative': [4, 5, 1, 3, 6, 2]}, {'Size': '2', 'Order': 6, 'Representative': [5, 1, 2, 6, 4, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['3', '1'], 'ConjugacyClass': 2}, {'RootOf': ['6067', '7', '-11', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [3, 3]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [6]}], 'Frobs': [3, 3, 4, 3, 4, 3, 3, 5, 6, 4, 1, 3, 5, 6, 3, 6, 5, 4, 3, 4, 6, 5, 3, 4, 3, 5, 6, 3, 4, 3, 3, 1, 2, 4, 5, 4, 6, 6, 6, 2, 1, 5, 5, 3, 6, 5, 4, 3, 6, 5, 6, 5, 4, 5, 3, 3, 5, 4, 3, 4, 6, 6, 3, 5, 3, 6, 1, 6, 6, 5, 3, 4, 3, 2, 4, 6, 4, 6, 4, 4, 4, 4, 5, 2, 5, 3, 4, 3, 4, 2, 2, 1, 2, 4, 5, 2, 5, 5, 2, 4, 2, 3, 6, 4, 4, 3, 6, 6, 4, 5, 2, 6, 2, 4, 1, 5, 2, 6, 3, 4, 4, 6, 6, 2, 4, 4, 4, 4, 2, 2, 4, 3, 4, 3, 5, 4, 2, 3, 3, 4, 4, 5, 3, 2, 4, 4, 3, 3, 5, 3, 6, 5, 2, 3, 6, 5, 1, 1, 2, 1, 6, 6, 6, 4, 3, 3, 5, 3], 'G-Gens': [[1, 5, 4, 3, 2, 6], [2, 1, 5, 6, 3, 4]], 'G-Name': 'D12', 'Polynomial': [-31, -13, 10, 5, 0, -3, 1], 'QpRts': [['-6623855', '8119967'], ['5002112', '8119967'], ['-3274541', '0'], ['-5002111', '-8119967'], ['3274542', '0'], ['6623856', '-8119967']], 'QpRts-minpoly': [2, 7, 1], 'QpRts-p': 11, 'QpRts-prec': 7, 'Size': 12, 'TransitiveDegree': 6}