Artin representation data - 2.405.12t18.a

Formats: - HTML - YAML - JSON - 2026-05-12T13:32:06.373261

• 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, 5], 'Baselabel': '2.405.12t18.a', 'CharacterField': 3, 'Conductor': 405, 'Container': '12t18', 'Dets': ['1.45.6t1.b.b', '1.45.6t1.b.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': [14, 19, 20, 16, 16, 15], '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]], [[1], [0, 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': [14, 19, 20, 16, 16, 15], '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]], [[1], [-1, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 11, 419], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, 1, 0, 0, 2, 0, 0, -1, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-1, 3, 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': '1.3.2t1.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': '1.15.2t1.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': '1.5.2t1.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': '1.45.6t1.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': 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': '1.9.6t1.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': '1.45.6t1.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': 2, 'Baselabel': '1.45.6t1.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': 2, 'Baselabel': '1.45.6t1.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': 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': '2.135.3t2.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': '2.135.6t3.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': '2.405.6t5.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': '2.405.6t5.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}, {'GalConj': 1, 'Baselabel': '2.405.12t18.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': '2.405.12t18.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': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9]}, {'Size': '3', 'Order': 2, 'Representative': [10, 9, 4, 3, 6, 5, 12, 11, 2, 1, 8, 7]}, {'Size': '3', 'Order': 2, 'Representative': [11, 12, 5, 6, 3, 4, 9, 10, 7, 8, 1, 2]}, {'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, 7, 8, 1, 2, 11, 12, 5, 6, 3, 4]}, {'Size': '2', 'Order': 3, 'Representative': [1, 6, 11, 4, 5, 10, 3, 8, 9, 2, 7, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 10, 7, 4, 5, 2, 11, 8, 9, 6, 3, 12]}, {'Size': '1', 'Order': 6, 'Representative': [4, 11, 2, 9, 12, 7, 10, 5, 8, 3, 6, 1]}, {'Size': '1', 'Order': 6, 'Representative': [12, 3, 10, 1, 8, 11, 6, 9, 4, 7, 2, 5]}, {'Size': '2', 'Order': 6, 'Representative': [12, 11, 2, 1, 8, 7, 10, 9, 4, 3, 6, 5]}, {'Size': '2', 'Order': 6, 'Representative': [8, 3, 10, 5, 4, 11, 6, 1, 12, 7, 2, 9]}, {'Size': '2', 'Order': 6, 'Representative': [8, 11, 2, 5, 4, 7, 10, 1, 12, 3, 6, 9]}, {'Size': '3', 'Order': 6, 'Representative': [6, 1, 12, 7, 2, 9, 8, 3, 10, 5, 4, 11]}, {'Size': '3', 'Order': 6, 'Representative': [2, 5, 8, 11, 10, 1, 4, 7, 6, 9, 12, 3]}, {'Size': '3', 'Order': 6, 'Representative': [3, 8, 9, 2, 7, 12, 1, 6, 11, 4, 5, 10]}, {'Size': '3', 'Order': 6, 'Representative': [7, 4, 1, 10, 11, 8, 5, 2, 3, 12, 9, 6]}], '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': ['36', '3', '1'], 'ConjugacyClass': 8}, {'RootOf': ['144', '-6', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-36', '1'], 'ConjugacyClass': 2}, {'RootOf': ['17496', '-972', '0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['27', '27', '0', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['459', '36', '1'], 'ConjugacyClass': 13}, {'RootOf': ['216', '27', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-3', '1'], 'ConjugacyClass': 6}, {'RootOf': ['36', '3', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['-36', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-27', '1'], 'ConjugacyClass': 11}, {'RootOf': ['1026', '-63', '1'], 'ConjugacyClass': 12}, {'RootOf': ['40041', '-837', '0', '1'], 'ConjugacyClass': 15}, {'RootOf': ['4563', '-513', '0', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-216', '108', '0', '1'], 'ConjugacyClass': 17}, {'RootOf': ['1728', '432', '0', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [14, 4, 15, 18, 16, 17, 12, 7, 13, 16, 8, 4, 15, 18, 11, 12, 15, 9, 17, 3, 4, 9, 14, 3, 18, 16, 17, 2, 7, 10, 4, 15, 14, 6, 15, 5, 17, 4, 13, 14, 3, 7, 16, 17, 12, 1, 8, 18, 14, 8, 2, 15, 9, 3, 13, 11, 3, 7, 18, 16, 17, 13, 4, 15, 18, 14, 5, 17, 10, 9, 11, 3, 18, 17, 7, 13, 16, 4, 15, 8, 15, 9, 3, 4, 9, 14, 3, 18, 16, 17, 12, 16, 4, 15, 8, 12, 15, 3, 4, 1, 18, 2, 10, 16, 8, 4, 14, 12, 15, 9, 17, 4, 13, 5, 7, 16, 17, 12, 13, 16, 6, 18, 11, 12, 9, 3, 5, 3, 18, 17, 7, 10, 8, 4, 15, 8, 12, 17, 13, 3, 1, 16, 17, 12, 1, 16, 18, 14, 8, 12, 17, 3, 4, 13, 18, 16, 1, 16, 4, 15, 14, 2, 17, 3, 10, 14, 7, 18], 'G-Gens': [[6, 1, 12, 7, 2, 9, 8, 3, 10, 5, 4, 11], [9, 10, 7, 8, 1, 2, 11, 12, 5, 6, 3, 4], [1, 6, 11, 4, 5, 10, 3, 8, 9, 2, 7, 12], [8, 7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9]], 'G-Name': 'C6*S3', 'Polynomial': [1, 0, 0, 1, 0, 0, 2, 0, 0, -1, 0, 0, 1], 'QpRts': [['362816744', '84331322', '203591624', '-14669268', '-351142913', '17034937'], ['-1894845', '-305573344', '-380597829', '-10005205', '327290484', '129036446'], ['283017799', '124577803', '241313106', '-180903136', '-68332899', '184215426'], ['-213576354', '-346891481', '353653054', '171957389', '-79804505', '-142239380'], ['-314396057', '17415311', '-30804612', '-131518292', '-125997533', '-380863843'], ['323779886', '-136302420', '229725025', '-148917879', '-7105082', '-233721782'], ['360654577', '-392659426', '135406750', '-83332984', '34207231', '-209533712'], ['-282836306', '-266110913', '-376451605', '190682211', '-86586958', '-154582588'], ['-48420687', '-101746633', '-172787012', '146187560', '-338590275', '363828906'], ['-321885041', '-373854957', '150872804', '158923084', '-320185402', '104685336'], ['172058345', '268081623', '-376719856', '264236120', '34125668', '25318286'], ['-319318061', '-202728327', '22798551', '-362639600', '166391463', '296821968']], 'QpRts-minpoly': [2, 11, 11, 10, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 8, 'Size': 36, 'TransitiveDegree': 12}