Artin representation data - 3.36100.12t33.a

Formats: - HTML - YAML - JSON - 2024-04-27T20:32:52.151420

• 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, 19], 'Baselabel': '3.36100.12t33.a', 'CharacterField': 5, 'Conductor': 36100, 'Container': '12t33', 'Dets': ['1.1.1t1.a.a', '1.1.1t1.a.a'], 'Dim': 3, 'GalConjSigns': [1, 1], 'Galn': 5, 'GaloisConjugates': [{'Sign': 1, 'Character': [[3], [-1], [0], [0, 0, -1, -1], [1, 0, 1, 1]], 'GalOrbIndex': 1, 'HardFactors': [6, 6, 3, 6], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [1], [-1], [-1]], [[1], [0], [0], [-1]], [[1], [0, 0, 1, 1], [0, 0, -1, -1], [-1]], [[1], [-1, 0, -1, -1], [1, 0, 1, 1], [-1]], [[1], [1]]]}, {'Sign': 1, 'Character': [[3], [-1], [0], [1, 0, 1, 1], [0, 0, -1, -1]], 'GalOrbIndex': 2, 'HardFactors': [6, 6, 3, 6], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [1], [-1], [-1]], [[1], [0], [0], [-1]], [[1], [-1, 0, -1, -1], [1, 0, 1, 1], [-1]], [[1], [0, 0, 1, 1], [0, 0, -1, -1], [-1]], [[1], [1]]]}], 'GaloisConjugatesSigns': [1, 1], 'GaloisLabel': '5T4', 'Galt': 4, 'HardPrimes': [2, 5, 13, 19], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-74, 64, 6, -11, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [60, 5], 'Proj_Polynomial': [-74, 64, 6, -11, -1, 1], 'Proj_nTj': [5, 4]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.36100.12t33.a', 'Character': [[3, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, -1], [1, 0, 1, 1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '3.36100.12t33.a', 'Character': [[3, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 1, 1], [0, 0, -1, -1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '4.13032100.5t4.a', 'Character': [[4], [0], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.52128400.6t12.a', 'Character': [[5], [1], [-1], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5]}, {'Size': '15', 'Order': 2, 'Representative': [2, 1, 4, 3, 5]}, {'Size': '20', 'Order': 3, 'Representative': [2, 3, 1, 4, 5]}, {'Size': '12', 'Order': 5, 'Representative': [2, 3, 4, 5, 1]}, {'Size': '12', 'Order': 5, 'Representative': [3, 1, 4, 5, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2]}, {'Data': [2, 3, 4, 5, 1], 'Classes': [{'RootOf': ['-46930', '1'], 'ConjugacyClass': 4}, {'RootOf': ['46930', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'ALT', 'CycleType': [5]}], 'Frobs': [2, 3, 2, 4, 4, 3, 5, 2, 3, 2, 3, 3, 3, 4, 3, 4, 4, 2, 5, 3, 3, 3, 3, 5, 3, 5, 2, 4, 3, 4, 5, 2, 5, 5, 3, 4, 5, 5, 4, 5, 3, 3, 5, 5, 2, 4, 5, 5, 2, 4, 2, 3, 5, 5, 4, 5, 4, 3, 3, 4, 2, 5, 4, 5, 4, 3, 3, 3, 3, 3, 4, 4, 3, 2, 2, 3, 5, 2, 2, 4, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 2, 5, 2, 4, 3, 5, 5, 4, 2, 2, 2, 1, 3, 2, 2, 3, 2, 4, 5, 2, 2, 4, 3, 4, 2, 2, 2, 3, 5, 5, 3, 4, 4, 3, 2, 3, 2, 3, 3, 5, 3, 5, 3, 3, 3, 2, 2, 2, 3, 3, 5, 2, 3, 4, 3, 3, 5, 5, 2, 3, 3, 2, 5, 5, 5, 5, 2, 3, 5, 2, 4, 2, 2, 5, 5, 2, 4, 2], 'G-Gens': [[2, 3, 1, 4, 5], [1, 2, 4, 5, 3]], 'G-Name': 'A5', 'Polynomial': [-74, 64, 6, -11, -1, 1], 'QpRts': [['21048361107626'], ['23060360102725'], ['8868405430094'], ['-24267791115441'], ['24904388669554']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 557, 'QpRts-prec': 5, 'Size': 60, 'TransitiveDegree': 5}