Formats: - HTML - YAML - JSON - 2026-10-15T19:48:14.769565
Query: /api/artin_field_data/?_offset=0

Table artin_field_data

Artin representations

Show schema

{'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.31.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.372.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [-1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.4464.6t3.b', 'Character': [[2], [-2], [-2], [2], [0], [0], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.31.3t2.b', 'Character': [[2], [2], [2], [2], [0], [0], [-1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.17856.4t5.b', 'Character': [[3], [3], [-1], [-1], [1], [1], [0], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.184512.6t11.a', 'Character': [[3], [-3], [1], [-1], [1], [-1], [0], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.5952.6t11.a', 'Character': [[3], [-3], [1], [-1], [-1], [1], [0], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.553536.6t8.b', 'Character': [[3], [3], [-1], [-1], [-1], [-1], [0], [1], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 6, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '1', 'Order': 2, 'Representative': [4, 5, 6, 1, 2, 3]}, {'Size': '3', 'Order': 2, 'Representative': [1, 2, 6, 4, 5, 3]}, {'Size': '3', 'Order': 2, 'Representative': [1, 5, 6, 4, 2, 3]}, {'Size': '6', 'Order': 2, 'Representative': [2, 1, 3, 5, 4, 6]}, {'Size': '6', 'Order': 2, 'Representative': [2, 1, 6, 5, 4, 3]}, {'Size': '8', 'Order': 3, 'Representative': [3, 1, 2, 6, 4, 5]}, {'Size': '6', 'Order': 4, 'Representative': [1, 3, 5, 4, 6, 2]}, {'Size': '6', 'Order': 4, 'Representative': [4, 3, 5, 1, 6, 2]}, {'Size': '8', 'Order': 6, 'Representative': [3, 1, 5, 6, 4, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-60264', '-3348', '-30', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-31933745856', '-1621560384', '-32961168', '-412128', '2124', '60', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-30', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-31933745856', '1621560384', '-32961168', '412128', '2124', '-60', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [3, 3]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [6]}], 'Frobs': [7, 5, 10, 10, 8, 8, 5, 10, 8, 9, 5, 8, 10, 9, 4, 5, 7, 6, 3, 7, 8, 5, 6, 5, 7, 10, 10, 7, 7, 10, 9, 4, 9, 9, 2, 9, 7, 10, 8, 3, 6, 6, 7, 7, 9, 9, 10, 9, 1, 8, 10, 6, 8, 8, 10, 6, 9, 5, 6, 10, 2, 3, 10, 7, 6, 10, 5, 6, 8, 4, 9, 7, 5, 7, 3, 6, 9, 7, 9, 8, 7, 7, 4, 6, 10, 7, 9, 8, 5, 5, 7, 7, 9, 8, 5, 7, 9, 2, 9, 7, 10, 9, 7, 5, 9, 4, 6, 10, 7, 8, 2, 6, 3, 5, 5, 5, 5, 8, 3, 7, 7, 8, 9, 7, 10, 10, 6, 6, 10, 7, 9, 8, 10, 8, 9, 7, 9, 5, 5, 9, 2, 5, 5, 8, 6, 1, 4, 3, 9, 6, 7, 5, 5, 7, 10, 8, 3, 9, 4, 5, 8, 5, 9, 4, 10, 8, 5, 7], 'G-Gens': [[2, 1, 3, 5, 4, 6], [1, 5, 3, 4, 2, 6], [3, 1, 2, 6, 4, 5]], 'G-Name': 'C2*S4', 'Polynomial': [93, 0, -17, 0, -5, 0, 1], 'QpRts': [['-616015802506173', '-4564588175696963'], ['-2623602326317665', '0'], ['-3085348778303676', '-4564588175696963'], ['616015802506173', '4564588175696963'], ['2623602326317665', '0'], ['3085348778303676', '4564588175696963']], 'QpRts-minpoly': [3, 16, 1], 'QpRts-p': 17, 'QpRts-prec': 13, 'Size': 48, 'TransitiveDegree': 6, 'id': 540290}