Formats: - HTML - YAML - JSON - 2026-10-07T07:03:18.675948
  • artin_reps • Show schema
    {'BadPrimes': [2, 5, 7], 'Baselabel': '2.2240.12t18.a', 'CharacterField': 3, 'Conductor': 2240, 'Container': '12t18', 'Dets': ['1.140.6t1.b.b', '1.140.6t1.b.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1], [2, 2], [0, -2], [-1, -1], [0, 1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 7, 20, 21, 16, 10], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [1], [1]], [[1], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [-1], [1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1]], [[1], [-1, -1]], [[1], [0, 1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1], [0, -2], [2, 2], [0, 1], [-1, -1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 7, 20, 21, 16, 10], '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], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [1], [1]], [[1], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [-1], [1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1]], [[1], [0, 1]], [[1], [-1, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 11, 229], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [9, 0, 20, 0, 22, 0, 16, 0, 9, 0, 4, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-13, 5, -1, 1], 'Proj_nTj': [3, 2]}
  • artin_field_data • Show schema
    {'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': '1.40.2t1.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': '1.20.2t1.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': '1.8.2t1.b', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.280.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.56.6t1.c', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [-1, -1], [0, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.140.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.140.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.7.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.7.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.280.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.56.6t1.c', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [0, 1], [-1, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.980.3t2.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': '2.15680.6t3.e', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.140.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.2240.12t18.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [2, 2], [0, -2], [-1, -1], [0, 1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.2240.12t18.a', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, -2], [2, 2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.140.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [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': [7, 8, 10, 9, 12, 11, 1, 2, 4, 3, 6, 5]}, {'Size': '3', 'Order': 2, 'Representative': [3, 5, 1, 6, 2, 4, 10, 12, 11, 7, 9, 8]}, {'Size': '3', 'Order': 2, 'Representative': [8, 7, 9, 10, 11, 12, 2, 1, 3, 4, 5, 6]}, {'Size': '1', 'Order': 3, 'Representative': [4, 3, 6, 5, 1, 2, 9, 10, 12, 11, 8, 7]}, {'Size': '1', 'Order': 3, 'Representative': [5, 6, 2, 1, 4, 3, 12, 11, 7, 8, 10, 9]}, {'Size': '2', 'Order': 3, 'Representative': [5, 2, 3, 1, 4, 6, 12, 8, 7, 10, 11, 9]}, {'Size': '2', 'Order': 3, 'Representative': [4, 2, 3, 5, 1, 6, 9, 8, 12, 10, 11, 7]}, {'Size': '2', 'Order': 3, 'Representative': [5, 3, 6, 1, 4, 2, 12, 10, 7, 11, 8, 9]}, {'Size': '1', 'Order': 6, 'Representative': [12, 11, 8, 7, 9, 10, 5, 6, 1, 2, 3, 4]}, {'Size': '1', 'Order': 6, 'Representative': [9, 10, 11, 12, 7, 8, 4, 3, 5, 6, 2, 1]}, {'Size': '2', 'Order': 6, 'Representative': [9, 8, 10, 12, 7, 11, 4, 2, 5, 3, 6, 1]}, {'Size': '2', 'Order': 6, 'Representative': [12, 8, 10, 7, 9, 11, 5, 2, 1, 3, 6, 4]}, {'Size': '2', 'Order': 6, 'Representative': [9, 11, 8, 12, 7, 10, 4, 6, 5, 2, 3, 1]}, {'Size': '3', 'Order': 6, 'Representative': [11, 12, 7, 8, 10, 9, 6, 5, 2, 1, 4, 3]}, {'Size': '3', 'Order': 6, 'Representative': [10, 9, 12, 11, 8, 7, 3, 4, 6, 5, 1, 2]}, {'Size': '3', 'Order': 6, 'Representative': [2, 5, 1, 3, 6, 4, 8, 12, 10, 7, 9, 11]}, {'Size': '3', 'Order': 6, 'Representative': [3, 1, 4, 6, 2, 5, 10, 7, 11, 9, 12, 8]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['2144', '24', '1'], 'ConjugacyClass': 7}, {'RootOf': ['2436', '8', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['24', '1'], 'ConjugacyClass': 2}, {'RootOf': ['13824', '-576', '36', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-13824', '-576', '-36', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['2436', '-8', '1'], 'ConjugacyClass': 12}, {'RootOf': ['2144', '-24', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-84', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-68', '1'], 'ConjugacyClass': 6}, {'RootOf': ['5796', '-152', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['68', '1'], 'ConjugacyClass': 10}, {'RootOf': ['84', '1'], 'ConjugacyClass': 11}, {'RootOf': ['5796', '152', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-108368', '2532', '120', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-290816', '768', '120', '1'], 'ConjugacyClass': 16}, {'RootOf': ['290816', '768', '-120', '1'], 'ConjugacyClass': 17}, {'RootOf': ['108368', '2532', '-120', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [6, 7, 18, 11, 16, 3, 16, 15, 12, 14, 17, 18, 9, 9, 10, 17, 16, 12, 7, 3, 16, 18, 9, 8, 4, 13, 12, 8, 13, 4, 2, 15, 16, 4, 12, 17, 17, 6, 14, 18, 16, 14, 18, 16, 3, 17, 4, 2, 5, 10, 15, 3, 5, 4, 15, 13, 13, 18, 17, 1, 5, 3, 9, 17, 15, 18, 15, 4, 7, 14, 16, 18, 13, 18, 4, 12, 11, 18, 8, 7, 4, 14, 17, 4, 18, 8, 9, 15, 2, 14, 8, 17, 11, 4, 15, 14, 12, 5, 6, 12, 9, 17, 7, 6, 16, 16, 1, 15, 17, 1, 12, 17, 4, 16, 3, 7, 1, 13, 18, 4, 13, 4, 18, 7, 15, 14, 12, 18, 14, 18, 16, 14, 18, 3, 6, 1, 17, 7, 3, 7, 4, 10, 13, 9, 11, 3, 3, 16, 15, 12, 18, 9, 1, 12, 7, 3, 18, 8, 4, 11, 8, 4, 14, 15, 16, 13, 17, 17], 'G-Gens': [[1, 6, 2, 4, 5, 3, 7, 11, 9, 8, 10, 12], [9, 8, 10, 12, 7, 11, 4, 2, 5, 3, 6, 1], [3, 5, 1, 6, 2, 4, 10, 12, 11, 7, 9, 8], [7, 8, 10, 9, 12, 11, 1, 2, 4, 3, 6, 5]], 'G-Name': 'C6*S3', 'Polynomial': [9, 0, 20, 0, 22, 0, 16, 0, 9, 0, 4, 0, 1], 'QpRts': [['-2913456152', '3185266774', '-977757610', '1732249505', '1006100397', '1354865971'], ['2621425138', '-549125477', '2572004854', '880337338', '-1001384036', '-976771553'], ['-2105525577', '-2251907225', '-381126504', '898103608', '695309307', '-1514208144'], ['-1598225153', '-429941695', '-3139604115', '-2380177888', '1965519443', '-2844663332'], ['3279711768', '-998501644', '-1546833770', '-1874533129', '-466701613', '150106962'], ['1558222674', '-2417901304', '-879316404', '2674854983', '2810992956', '1151289298'], ['2913456152', '-3185266774', '977757610', '-1732249505', '-1006100397', '-1354865971'], ['-2621425138', '549125477', '-2572004854', '-880337338', '1001384036', '976771553'], ['1598225153', '429941695', '3139604115', '2380177888', '-1965519443', '2844663332'], ['2105525577', '2251907225', '381126504', '-898103608', '-695309307', '1514208144'], ['-1558222674', '2417901304', '879316404', '-2674854983', '-2810992956', '-1151289298'], ['-3279711768', '998501644', '1546833770', '1874533129', '466701613', '-150106962']], 'QpRts-minpoly': [3, 3, 10, 0, 2, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 8, 'Size': 36, 'TransitiveDegree': 12}