LMFDB - Artin representation data - 14.5362361725268781105601.21t38.a

Formats: - HTML - YAML - JSON - 2024-04-25T14:40:00.397991

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': [461, 587], 'Baselabel': '14.5362361725268781105601.21t38.a', 'CharacterField': 1, 'Conductor': 5362361725268781105601, 'Container': '21t38', 'Dets': ['1.1.1t1.a.a'], 'Dim': 14, 'GalConjSigns': [1], 'Galn': 7, 'GaloisConjugates': [{'Sign': 1, 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [16, 17], 'LocalFactors': [[[1], [-14], [91], [-364], [1001], [-2002], [3003], [-3432], [3003], [-2002], [1001], [-364], [91], [-14], [1]], [[1], [-6], [11], [4], [-39], [38], [27], [-72], [27], [38], [-39], [4], [11], [-6], [1]], [[1], [-2], [-5], [12], [9], [-30], [-5], [40], [-5], [-30], [9], [12], [-5], [-2], [1]], [[1], [-2], [-5], [12], [9], [-30], [-5], [40], [-5], [-30], [9], [12], [-5], [-2], [1]], [[1], [-2], [1], [-4], [8], [-4], [6], [-12], [6], [-4], [8], [-4], [1], [-2], [1]], [[1], [1], [1], [-4], [-4], [-4], [6], [6], [6], [-4], [-4], [-4], [1], [1], [1]], [[1], [0], [-1], [0], [-3], [0], [3], [0], [3], [0], [-3], [0], [-1], [0], [1]], [[1], [0], [-1], [0], [-3], [0], [3], [0], [3], [0], [-3], [0], [-1], [0], [1]], [[1], [1], [1], [1], [1], [-2], [-2], [-2], [-2], [-2], [1], [1], [1], [1], [1]], [[1], [-2], [1], [0], [0], [0], [-2], [4], [-2], [0], [0], [0], [1], [-2], [1]], [[1], [0], [-1], [-2], [0], [2], [0], [0], [0], [2], [0], [-2], [-1], [0], [1]], [[1], [1], [1], [0], [0], [0], [-2], [-2], [-2], [0], [0], [0], [1], [1], [1]], [[1], [0], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [0], [1]], [[1], [-1], [1], [-1], [1], [-2], [2], [-2], [2], [-2], [1], [-1], [1], [-1], [1]], [[1], [0], [-1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-1], [0], [1]], [[1], [0], [-1], [0], [-2], [0], [2], [0], [1], [0], [-1]], [[1], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '7T7', 'Galt': 7, 'HardPrimes': [461, 587], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-1, 2, -2, 2, -3, 1, -1, 1], 'NumBadPrimes': 2, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [-1, 2, -2, 2, -3, 1, -1, 1], 'Proj_nTj': [7, 7]}

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], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.270607.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [-1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.1451092619389809048643369807.14t46.a', 'Character': [[6], [-4], [0], [2], [3], [0], [-2], [0], [1], [-1], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.270607.7t7.a', 'Character': [[6], [4], [0], [2], [3], [0], [2], [0], [1], [-1], [1], [0], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.5362361725268781105601.21t38.a', 'Character': [[14], [6], [2], [2], [2], [-1], [0], [0], [-1], [2], [0], [-1], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.2105669790047577227763562874854558114371152180559217249.42t413.a', 'Character': [[14], [-6], [-2], [2], [2], [-1], [0], [0], [-1], [2], [0], [1], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.7781283522035931176072913394164076000883761989007.30t565.a', 'Character': [[14], [-4], [0], [2], [-1], [2], [2], [0], [-1], [-1], [-1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '14.1451092619389809048643369807.30t565.a', 'Character': [[14], [4], [0], [2], [-1], [2], [-2], [0], [-1], [-1], [1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.1451092619389809048643369807.42t412.a', 'Character': [[15], [5], [-3], [-1], [3], [0], [1], [-1], [0], [-1], [-1], [0], [1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '15.2105669790047577227763562874854558114371152180559217249.42t411.a', 'Character': [[15], [-5], [3], [-1], [3], [0], [-1], [-1], [0], [-1], [1], [0], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '20.2105669790047577227763562874854558114371152180559217249.70.a', 'Character': [[20], [0], [0], [-4], [2], [2], [0], [0], [0], [2], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.2105669790047577227763562874854558114371152180559217249.84.a', 'Character': [[21], [1], [-3], [1], [-3], [0], [-1], [-1], [1], [1], [1], [0], [0], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '21.569808984875404730873414458875767407655634378124588102100143.42t418.a', 'Character': [[21], [-1], [3], [1], [-3], [0], [1], [-1], [1], [1], [-1], [0], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.4433845264719007962389630809295253268495884058832752249973222046191881956662725508377278574432629571579128001.126.a', 'Character': [[35], [-5], [-1], [-1], [-1], [-1], [1], [1], [0], [-1], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '35.3055521891210128111655718285133503873449573681186471599721549819231881705560200943.70.a', 'Character': [[35], [5], [1], [-1], [-1], [-1], [-1], [1], [0], [-1], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7]}, {'Size': '21', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 7]}, {'Size': '105', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 7]}, {'Size': '105', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6, 7]}, {'Size': '70', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6, 7]}, {'Size': '280', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4, 7]}, {'Size': '210', 'Order': 4, 'Representative': [2, 3, 4, 1, 5, 6, 7]}, {'Size': '630', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5, 7]}, {'Size': '504', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6, 7]}, {'Size': '210', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 7, 6]}, {'Size': '420', 'Order': 6, 'Representative': [2, 3, 1, 5, 4, 6, 7]}, {'Size': '840', 'Order': 6, 'Representative': [2, 3, 4, 5, 6, 1, 7]}, {'Size': '720', 'Order': 7, 'Representative': [2, 3, 4, 5, 6, 7, 1]}, {'Size': '504', 'Order': 10, 'Representative': [2, 3, 4, 5, 1, 7, 6]}, {'Size': '420', 'Order': 12, 'Representative': [2, 3, 4, 1, 6, 7, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 4]}, {'Data': 0, 'Classes': 11, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 5]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 2, 4]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 3, 3]}, {'Data': 0, 'Classes': 12, 'Algorithm': 'CYC', 'CycleType': [1, 6]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [2, 2, 3]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [2, 5]}, {'Data': 0, 'Classes': 15, 'Algorithm': 'CYC', 'CycleType': [3, 4]}, {'Data': 0, 'Classes': 13, 'Algorithm': 'CYC', 'CycleType': [7]}], 'Frobs': [13, 15, 15, 12, 10, 6, 13, 15, 11, 11, 15, 13, 11, 9, 12, 6, 4, 15, 13, 13, 9, 15, 14, 6, 12, 14, 15, 12, 12, 13, 8, 9, 9, 12, 11, 9, 14, 13, 10, 8, 15, 4, 8, 9, 14, 9, 12, 13, 12, 6, 12, 10, 8, 6, 15, 12, 14, 13, 8, 13, 11, 12, 10, 9, 14, 15, 15, 13, 6, 15, 8, 8, 12, 14, 15, 5, 13, 13, 12, 12, 15, 11, 13, 8, 9, 4, 8, 5, 7, 9, 15, 8, 12, 13, 13, 8, 6, 13, 15, 12, 13, 12, 9, 7, 7, 13, 9, 12, 8, 9, 6, 15, 13, 7, 6, 15, 8, 9, 12, 7, 3, 11, 9, 5, 12, 14, 9, 15, 14, 15, 14, 8, 15, 9, 5, 6, 13, 4, 9, 8, 12, 7, 15, 12, 15, 12, 3, 12, 3, 12, 13, 3, 9, 12, 8, 15, 11, 11, 8, 14, 9, 12, 13, 12, 8, 12, 11, 8], 'G-Gens': [[2, 3, 4, 5, 6, 7, 1], [2, 1, 3, 4, 5, 6, 7]], 'G-Name': 'S7', 'Polynomial': [-1, 2, -2, 2, -3, 1, -1, 1], 'QpRts': [['-51584465', '0'], ['259574686', '0'], ['-95638514', '174264094'], ['-175969747', '0'], ['-194015780', '-174264094'], ['-11789299', '-17174771'], ['269423120', '17174771']], 'QpRts-minpoly': [2, 58, 1], 'QpRts-p': 59, 'QpRts-prec': 5, 'Size': 5040, 'TransitiveDegree': 7}

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Elliptic curves over $\Q$
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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.