Database - artin_field_data (Artin representations)

Formats: - HTML - YAML - JSON - 2026-04-29T23:21:43.472418

Query: /api/artin_field_data/?_offset=0

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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.21.2t1.a', 'Character': [[1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.105.2t1.a', 'Character': [[1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.11025.8t5.a', 'Character': [[2], [-2], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [2, 1, 7, 8, 6, 5, 3, 4]}, {'Size': '2', 'Order': 4, 'Representative': [8, 4, 5, 1, 7, 3, 6, 2]}, {'Size': '2', 'Order': 4, 'Representative': [5, 6, 4, 7, 2, 1, 8, 3]}, {'Size': '2', 'Order': 4, 'Representative': [3, 7, 2, 5, 8, 4, 1, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['8', '1'], 'ConjugacyClass': 3}, {'RootOf': ['10', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-55', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [4, 4]}], 'Frobs': [5, 3, 1, 3, 4, 5, 3, 4, 5, 4, 4, 3, 1, 3, 3, 5, 2, 4, 3, 4, 5, 1, 3, 1, 5, 1, 5, 5, 1, 5, 3, 2, 5, 4, 4, 1, 5, 3, 3, 3, 4, 4, 4, 3, 5, 4, 2, 5, 3, 4, 5, 4, 4, 1, 3, 5, 1, 4, 3, 4, 5, 3, 5, 2, 5, 5, 2, 3, 5, 4, 3, 4, 5, 3, 2, 3, 4, 5, 4, 4, 1, 2, 4, 5, 4, 5, 4, 3, 2, 3, 3, 1, 3, 4, 2, 3, 1, 2, 5, 2, 3, 5, 3, 4, 1, 5, 3, 3, 4, 4, 5, 3, 5, 4, 2, 4, 5, 3, 5, 4, 4, 3, 3, 5, 4, 4, 2, 2, 5, 5, 2, 5, 2, 3, 2, 4, 3, 5, 3, 4, 4, 4, 3, 5, 4, 2, 5, 3, 4, 5, 3, 1, 3, 3, 3, 4, 1, 1, 5, 1, 5, 5, 3, 1, 5, 3, 2, 5], 'G-Gens': [[5, 6, 4, 7, 2, 1, 8, 3], [2, 1, 7, 8, 6, 5, 3, 4], [8, 4, 5, 1, 7, 3, 6, 2]], 'G-Name': 'Q8', 'Polynomial': [-395, 1345, -1090, -305, 361, 29, -34, -1, 1], 'QpRts': [['-218737491'], ['-1520283893'], ['1015406775'], ['998045281'], ['1448893150'], ['617852891'], ['-851210477'], ['-1489966235']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 79, 'QpRts-prec': 5, 'Size': 8, 'TransitiveDegree': 8, 'id': 447334}