Artin representation data - 2.1296.12t18.a

Formats: - HTML - YAML - JSON - 2026-04-16T15:09:20.869182

• 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': '2.1296.12t18.a', 'CharacterField': 3, 'Conductor': 1296, 'Container': '12t18', 'Dets': ['1.9.6t1.a.b', '1.9.6t1.a.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [-1], [0, -1], [1, 1], [0, -2], [2, 2], [1], [0, 1], [-1, -1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 19, 16, 16, 16, 3], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [1], [1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [-1], [1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [-1], [1, 1], [0, -1], [2, 2], [0, -2], [1], [-1, -1], [0, 1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 19, 16, 16, 16, 3], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [1], [1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [-1], [1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 311, 347, 431], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [4, 0, 0, -4, 0, 0, 2, 0, 0, -2, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-2, 0, 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], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.12.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-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], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.36.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.36.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.36.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.36.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.108.3t2.b', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.432.6t3.a', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.324.6t5.c', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [0, -1], [1, 1], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.324.6t5.c', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [1, 1], [0, -1], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.1296.12t18.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [0, -1], [1, 1], [0, -2], [2, 2], [1, 0], [0, 1], [-1, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.1296.12t18.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [1, 1], [0, -1], [2, 2], [0, -2], [1, 0], [-1, -1], [0, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9]}, {'Size': '3', 'Order': 2, 'Representative': [2, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]}, {'Size': '1', 'Order': 3, 'Representative': [9, 6, 11, 8, 1, 10, 3, 12, 5, 2, 7, 4]}, {'Size': '1', 'Order': 3, 'Representative': [5, 10, 7, 12, 9, 2, 11, 4, 1, 6, 3, 8]}, {'Size': '2', 'Order': 3, 'Representative': [9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '2', 'Order': 3, 'Representative': [1, 6, 3, 8, 5, 10, 7, 12, 9, 2, 11, 4]}, {'Size': '2', 'Order': 3, 'Representative': [1, 10, 3, 12, 5, 2, 7, 4, 9, 6, 11, 8]}, {'Size': '1', 'Order': 6, 'Representative': [11, 4, 1, 6, 3, 8, 5, 10, 7, 12, 9, 2]}, {'Size': '1', 'Order': 6, 'Representative': [3, 12, 5, 2, 7, 4, 9, 6, 11, 8, 1, 10]}, {'Size': '2', 'Order': 6, 'Representative': [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2]}, {'Size': '2', 'Order': 6, 'Representative': [7, 12, 9, 2, 11, 4, 1, 6, 3, 8, 5, 10]}, {'Size': '2', 'Order': 6, 'Representative': [7, 4, 9, 6, 11, 8, 1, 10, 3, 12, 5, 2]}, {'Size': '3', 'Order': 6, 'Representative': [8, 3, 6, 1, 4, 11, 2, 9, 12, 7, 10, 5]}, {'Size': '3', 'Order': 6, 'Representative': [4, 7, 2, 5, 12, 3, 10, 1, 8, 11, 6, 9]}, {'Size': '3', 'Order': 6, 'Representative': [2, 9, 12, 7, 10, 5, 8, 3, 6, 1, 4, 11]}, {'Size': '3', 'Order': 6, 'Representative': [10, 1, 8, 11, 6, 9, 4, 7, 2, 5, 12, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['144', '-12', '1'], 'ConjugacyClass': 8}, {'RootOf': ['36', '6', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 2}, {'RootOf': ['0', '0', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['93312', '0', '0', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['144', '12', '1'], 'ConjugacyClass': 13}, {'RootOf': ['36', '-6', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-6', '1'], 'ConjugacyClass': 5}, {'RootOf': ['12', '1'], 'ConjugacyClass': 6}, {'RootOf': ['36', '6', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['24', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-12', '1'], 'ConjugacyClass': 11}, {'RootOf': ['144', '12', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-432', '0', '0', '1'], 'ConjugacyClass': 15}, {'RootOf': ['3456', '0', '0', '1'], 'ConjugacyClass': 16}, {'RootOf': ['27648', '0', '0', '1'], 'ConjugacyClass': 17}, {'RootOf': ['148176', '0', '0', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [15, 2, 16, 13, 17, 9, 3, 12, 18, 15, 11, 7, 16, 10, 17, 3, 18, 8, 14, 4, 7, 13, 17, 3, 8, 15, 14, 4, 1, 16, 2, 18, 15, 14, 16, 13, 5, 12, 18, 15, 4, 7, 17, 9, 3, 12, 14, 10, 17, 5, 3, 18, 8, 4, 16, 17, 3, 12, 6, 15, 11, 16, 2, 18, 8, 15, 13, 9, 18, 8, 15, 4, 13, 9, 12, 18, 15, 1, 16, 9, 18, 8, 4, 1, 10, 17, 3, 6, 15, 14, 4, 17, 12, 18, 11, 4, 16, 3, 12, 7, 13, 3, 18, 15, 14, 7, 17, 3, 18, 6, 14, 7, 16, 13, 12, 15, 11, 4, 16, 17, 9, 8, 15, 4, 10, 3, 8, 4, 10, 5, 2, 18, 14, 7, 16, 9, 3, 14, 16, 3, 2, 15, 14, 4, 7, 17, 8, 15, 14, 4, 9, 3, 12, 18, 13, 17, 2, 15, 7, 16, 17, 3, 14, 4, 16, 17, 12, 6], 'G-Gens': [[9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8], [1, 6, 3, 8, 5, 10, 7, 12, 9, 2, 11, 4], [8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9], [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]], 'G-Name': 'C6*S3', 'Polynomial': [4, 0, 0, -4, 0, 0, 2, 0, 0, -2, 0, 0, 1], 'QpRts': [['391502250', '26934478', '177487805', '-48011873', '389591751', '-276218132'], ['-262525226', '262993355', '226412071', '-317530148', '-340767976', '-230082613'], ['-285933862', '-358667786', '306972002', '51743266', '-376609137', '350948357'], ['217202666', '125607094', '7947182', '-35678142', '201944996', '-55691370'], ['98473961', '167353021', '-157202106', '-50638701', '185998638', '-226429155'], ['42035845', '260855364', '52970110', '-438670259', '382199090', '-439924299'], ['-195272983', '-6342927', '-64420790', '-290474004', '66505896', '-53544183'], ['-329067026', '414491494', '85374166', '267531996', '-187636989', '-95307290'], ['403895528', '-194287499', '-20285699', '98650574', '318281350', '-391224452'], ['220489381', '370023020', '-279382181', '-137671332', '-41431114', '-223864827'], ['-412664894', '365010713', '-242551212', '238730738', '310103241', '-297404174'], ['111864360', '353773151', '-93321348', '-231853854', '-14308007', '150998660']], 'QpRts-minpoly': [2, 6, 17, 17, 0, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 7, 'Size': 36, 'TransitiveDegree': 12}