Database - artin_field_data (Artin representations)

Formats: - HTML - YAML - JSON - 2025-12-20T08:41:41.995091

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': '1.451.5t1.c', 'Character': [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '1.451.5t1.c', 'Character': [[1, 0, 0, 0], [0, 0, 1, 0], [-1, -1, -1, -1], [0, 1, 0, 0], [0, 0, 0, 1]], 'CharacterField': 5}, {'GalConj': 3, 'Baselabel': '1.451.5t1.c', 'Character': [[1, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [-1, -1, -1, -1], [0, 0, 1, 0]], 'CharacterField': 5}, {'GalConj': 4, 'Baselabel': '1.451.5t1.c', 'Character': [[1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]], 'CharacterField': 5}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5]}, {'Size': '1', 'Order': 5, 'Representative': [2, 3, 5, 1, 4]}, {'Size': '1', 'Order': 5, 'Representative': [3, 5, 4, 2, 1]}, {'Size': '1', 'Order': 5, 'Representative': [5, 4, 1, 3, 2]}, {'Size': '1', 'Order': 5, 'Representative': [4, 1, 2, 5, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1822', '1'], 'ConjugacyClass': 2}, {'RootOf': ['1371', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-1786', '1'], 'ConjugacyClass': 4}, {'RootOf': ['18', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [5]}], 'Frobs': [3, 3, 3, 1, 1, 3, 1, 5, 4, 5, 4, 5, 1, 4, 1, 1, 2, 4, 2, 1, 4, 5, 2, 3, 1, 2, 1, 5, 1, 2, 3, 5, 2, 1, 3, 1, 5, 5, 5, 3, 4, 1, 4, 3, 5, 4, 3, 1, 1, 4, 3, 5, 2, 1, 3, 5, 5, 1, 4, 5, 4, 2, 3, 2, 3, 4, 1, 4, 4, 5, 3, 3, 2, 2, 1, 5, 1, 4, 2, 5, 1, 2, 2, 2, 2, 2, 3, 5, 5, 2, 4, 5, 4, 4, 1, 2, 2, 5, 1, 4, 3, 3, 4, 4, 1, 2, 2, 3, 4, 4, 4, 1, 4, 4, 1, 4, 5, 5, 4, 1, 2, 4, 4, 1, 3, 4, 3, 1, 5, 5, 5, 3, 1, 2, 3, 5, 1, 1, 5, 1, 3, 4, 5, 2, 4, 5, 1, 2, 4, 5, 5, 3, 5, 5, 3, 5, 1, 2, 3, 5, 2, 3, 5, 1, 2, 4, 3, 2], 'G-Gens': [[2, 3, 5, 1, 4]], 'G-Name': 'C5', 'Polynomial': [2551, 3875, -415, -180, -1, 1], 'QpRts': [['-401964'], ['668207'], ['-385282'], ['-204754'], ['323794']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 17, 'QpRts-prec': 5, 'Size': 5, 'TransitiveDegree': 5, 'id': 192683}