LMFDB - Artin representation data

Formats: - HTML - YAML - JSON - 2024-11-28T12:34:00.794343

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[]

artin_reps • Show schema

{'BadPrimes': [5, 29], 'Baselabel': '2.145.8t17.d', 'CharacterField': 4, 'Conductor': 145, 'Container': '8t17', 'Dets': ['1.145.4t1.b.a', '1.145.4t1.b.b'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, -2], [0, 2], [0], [1, -1], [1, 1], [-1, 1], [-1, -1], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [13, 15, 10, 15, 13, 13, 11, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, 2], [-1]], [[1], [0, -2], [-1]], [[1], [0], [1]], [[1], [-1, 1], [0, -1]], [[1], [-1, -1], [0, 1]], [[1], [1, -1], [0, -1]], [[1], [1, 1], [0, 1]], [[1], [0], [1]], [[1], [0], [0, 1]], [[1], [0], [0, -1]], [[1], [0, 1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [0, -2], [0], [1, 1], [1, -1], [-1, -1], [-1, 1], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [13, 15, 10, 15, 13, 13, 11, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1]], [[1], [0, 2], [-1]], [[1], [0], [1]], [[1], [-1, -1], [0, 1]], [[1], [-1, 1], [0, -1]], [[1], [1, 1], [0, 1]], [[1], [1, -1], [0, -1]], [[1], [0], [1]], [[1], [0], [0, -1]], [[1], [0], [0, 1]], [[1], [0, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '8T17', 'Galt': 17, 'HardPrimes': [2, 5, 7, 29, 37, 617, 643, 1609], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 1, -6, 11, -7, -1, 5, -4, 1], 'NumBadPrimes': 2, 'Proj_GAP': [8, 3], 'Proj_Polynomial': [11, -1, 6, -1, 1], 'Proj_nTj': [4, 3]}

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

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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.145.2t1.a', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.29.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [0, -1], [0, 1], [0, -1], [-1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.145.4t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [1, 0], [0, -1], [0, 1], [0, -1], [0, 1], [1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.5.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [1, 0], [-1, 0], [-1, 0], [1, 0], [0, -1], [0, 1], [0, -1], [0, 1], [-1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.145.4t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [0, -1], [0, 1], [0, -1], [1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.725.4t3.c', 'Character': [[2], [2], [-2], [0], [2], [2], [-2], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.145.4t3.a', 'Character': [[2], [2], [2], [0], [-2], [-2], [-2], [0], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.725.8t17.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, -2], [0, 2], [0, 0], [-1, 1], [-1, -1], [1, -1], [1, 1], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.725.8t17.b', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [0, -2], [0, 0], [-1, -1], [-1, 1], [1, 1], [1, -1], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.145.8t17.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, -2], [0, 2], [0, 0], [1, -1], [1, 1], [-1, 1], [-1, -1], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.145.8t17.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [0, -2], [0, 0], [1, 1], [1, -1], [-1, -1], [-1, 1], [0, 0], [0, 0], [0, 0]], 'CharacterField': 4}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [8, 7, 6, 5, 4, 3, 2, 1]}, {'Size': '2', 'Order': 2, 'Representative': [1, 7, 3, 5, 4, 6, 2, 8]}, {'Size': '4', 'Order': 2, 'Representative': [4, 3, 2, 1, 8, 7, 6, 5]}, {'Size': '1', 'Order': 4, 'Representative': [6, 4, 1, 7, 2, 8, 5, 3]}, {'Size': '1', 'Order': 4, 'Representative': [3, 5, 8, 2, 7, 1, 4, 6]}, {'Size': '2', 'Order': 4, 'Representative': [6, 5, 1, 2, 7, 8, 4, 3]}, {'Size': '2', 'Order': 4, 'Representative': [1, 4, 3, 7, 2, 6, 5, 8]}, {'Size': '2', 'Order': 4, 'Representative': [1, 5, 3, 2, 7, 6, 4, 8]}, {'Size': '2', 'Order': 4, 'Representative': [8, 5, 6, 2, 7, 3, 4, 1]}, {'Size': '2', 'Order': 4, 'Representative': [8, 4, 6, 7, 2, 3, 5, 1]}, {'Size': '4', 'Order': 4, 'Representative': [5, 3, 7, 1, 8, 2, 6, 4]}, {'Size': '4', 'Order': 8, 'Representative': [7, 3, 4, 1, 8, 5, 6, 2]}, {'Size': '4', 'Order': 8, 'Representative': [5, 1, 7, 6, 3, 2, 8, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-1412', '-6', '1'], 'ConjugacyClass': 8}, {'RootOf': ['-805', '-17', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1', '1'], 'ConjugacyClass': 2}, {'RootOf': ['3301', '-708', '154', '-12', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-265', '68', '1'], 'ConjugacyClass': 10}, {'RootOf': ['683', '79', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [2, 2, 4]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['21', '1'], 'ConjugacyClass': 5}, {'RootOf': ['10', '1'], 'ConjugacyClass': 6}, {'RootOf': ['175', '31', '1'], 'ConjugacyClass': 7}, {'RootOf': ['186941', '27218', '1839', '62', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['988733696406', '-2199713329', '3200076', '-2134', '1'], 'ConjugacyClass': 13}, {'RootOf': ['1051115460266', '-2321842149', '3314536', '-2134', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [13, 14, 8, 10, 4, 9, 13, 12, 11, 5, 4, 13, 4, 14, 13, 11, 6, 4, 8, 7, 14, 12, 9, 12, 13, 4, 11, 8, 3, 14, 13, 4, 13, 3, 3, 7, 13, 14, 8, 9, 3, 7, 4, 14, 10, 5, 4, 9, 10, 12, 11, 6, 7, 4, 10, 14, 12, 4, 10, 2, 9, 14, 13, 4, 9, 13, 4, 13, 8, 5, 9, 12, 13, 9, 12, 11, 12, 8, 7, 12, 5, 4, 2, 14, 6, 14, 12, 10, 4, 11, 13, 12, 10, 4, 3, 14, 3, 2, 11, 4, 8, 8, 14, 12, 1, 13, 8, 9, 12, 4, 13, 9, 13, 12, 1, 4, 11, 10, 14, 12, 7, 11, 13, 9, 7, 7, 3, 6, 13, 14, 12, 14, 4, 13, 7, 12, 14, 10, 13, 12, 2, 1, 14, 13, 12, 12, 14, 10, 12, 9, 10, 4, 11, 13, 13, 4, 6, 3, 8, 1, 13, 11, 13, 4, 8, 14, 7, 13], 'G-Gens': [[8, 7, 6, 5, 4, 3, 2, 1], [4, 3, 2, 1, 8, 7, 6, 5], [1, 4, 3, 7, 2, 6, 5, 8], [1, 7, 3, 5, 4, 6, 2, 8], [6, 5, 1, 2, 7, 8, 4, 3]], 'G-Name': 'C4wrC2', 'Polynomial': [1, 1, -6, 11, -7, -1, 5, -4, 1], 'QpRts': [['4774481353243894978925'], ['2726087502851369475327'], ['1212294133647330140931'], ['-69661304804273479165'], ['69661304804273479166'], ['-1212294133647330140930'], ['-2726087502851369475326'], ['-4774481353243894978924']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 571, 'QpRts-prec': 8, 'Size': 32, 'TransitiveDegree': 8}

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.