Artin representation data - 4.6581.5t5.a

Formats: - HTML - YAML - JSON - 2025-01-26T08:03:58.345298

• 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': [6581], 'Baselabel': '4.6581.5t5.a', 'CharacterField': 1, 'Conductor': 6581, 'Container': '5t5', 'Dets': ['1.6581.2t1.a.a'], 'Dim': 4, 'GalConjSigns': [1], 'Galn': 5, 'GaloisConjugates': [{'Sign': 1, 'Character': [[4], [2], [0], [1], [0], [-1], [-1]], 'GalOrbIndex': 1, 'HardFactors': [8], 'LocalFactors': [[[1], [-4], [6], [-4], [1]], [[1], [-2], [0], [2], [-1]], [[1], [0], [-2], [0], [1]], [[1], [-1], [0], [-1], [1]], [[1], [0], [0], [0], [-1]], [[1], [1], [1], [1], [1]], [[1], [1], [0], [-1], [-1]], [[1], [-1], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '5T5', 'Galt': 5, 'HardPrimes': [6581], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-1, 0, -2, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [120, 34], 'Proj_Polynomial': [-1, 0, -2, 0, 0, 1], 'Proj_nTj': [5, 5]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.6581.2t1.a', 'Character': [[1], [-1], [1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.285020220941.10t12.a', 'Character': [[4], [-2], [0], [1], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.6581.5t5.a', 'Character': [[4], [2], [0], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.43309561.10t13.a', 'Character': [[5], [1], [1], [-1], [-1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.285020220941.6t14.a', 'Character': [[5], [-1], [1], [-1], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.285020220941.20t30.a', 'Character': [[6], [0], [-2], [0], [0], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5]}, {'Size': '10', 'Order': 2, 'Representative': [2, 1, 3, 4, 5]}, {'Size': '15', 'Order': 2, 'Representative': [2, 1, 4, 3, 5]}, {'Size': '20', 'Order': 3, 'Representative': [2, 3, 1, 4, 5]}, {'Size': '30', 'Order': 4, 'Representative': [2, 3, 4, 1, 5]}, {'Size': '24', 'Order': 5, 'Representative': [2, 3, 4, 5, 1]}, {'Size': '20', 'Order': 6, 'Representative': [2, 3, 1, 5, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 4]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [2, 3]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [5]}], 'Frobs': [5, 7, 6, 3, 6, 6, 6, 6, 3, 5, 6, 5, 4, 7, 4, 4, 5, 5, 4, 6, 7, 5, 5, 3, 5, 6, 6, 5, 7, 5, 3, 2, 7, 5, 4, 4, 4, 6, 5, 5, 5, 6, 7, 7, 5, 6, 5, 5, 3, 3, 7, 6, 5, 5, 2, 6, 4, 3, 6, 4, 5, 4, 4, 3, 4, 7, 7, 2, 5, 5, 7, 5, 5, 5, 6, 2, 5, 4, 5, 7, 5, 6, 3, 2, 5, 7, 6, 5, 5, 5, 4, 5, 5, 2, 5, 3, 6, 7, 3, 2, 5, 5, 5, 7, 5, 7, 6, 6, 5, 4, 6, 7, 7, 5, 7, 5, 5, 2, 6, 7, 4, 7, 3, 2, 7, 6, 2, 2, 2, 6, 2, 2, 2, 6, 3, 4, 7, 4, 7, 3, 6, 5, 6, 7, 6, 6, 4, 2, 2, 5, 5, 5, 3, 7, 6, 7, 7, 6, 7, 3, 2, 5, 3, 6, 5, 5, 4, 7], 'G-Gens': [[2, 1, 3, 4, 5], [2, 3, 4, 5, 1]], 'G-Name': 'S5', 'Polynomial': [-1, 0, -2, 0, 0, 1], 'QpRts': [['-8306', '0'], ['3365', '1368'], ['5846', '318'], ['-4843', '-1368'], ['3938', '-318']], 'QpRts-minpoly': [3, 6, 1], 'QpRts-p': 7, 'QpRts-prec': 5, 'Size': 120, 'TransitiveDegree': 5}