LMFDB - Artin representation data

Formats: - HTML - YAML - JSON - 2025-04-07T00:21:19.959577

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': [2, 5, 19], 'Baselabel': '2.3040.12t18.d', 'CharacterField': 3, 'Conductor': 3040, 'Container': '12t18', 'Dets': ['1.760.6t1.b.b', '1.760.6t1.b.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 18, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [-1], [0, -1], [1, 1], [2, 2], [0, -2], [1], [-1, -1], [0, 1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 20, 7, 12, 20, 16, 9, 15, 3, 3, 12, 3, 1, 3, 1, 3, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [1], [1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [-1], [1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1]], [[1], [-1, -1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [-1], [1, 1], [0, -1], [0, -2], [2, 2], [1], [0, 1], [-1, -1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 20, 7, 12, 20, 16, 9, 15, 3, 3, 12, 3, 1, 3, 1, 3, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [1], [1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [0, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [-1], [1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '18T6', 'Galt': 6, 'HardPrimes': [2, 5, 7, 11, 19, 29, 41, 79, 107, 227, 373, 467, 809, 1901, 2887, 4523, 23292837615942649], 'Hide': 1, 'Indicator': 0, 'Is_Even': False, 'NFGal': [68921, -127756, 97785, -58082, 39442, -10038, -13003, 2468, 7265, -232, -1417, -978, 431, 90, 42, -26, -2, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [26, -6, -1, 1], 'Proj_nTj': [3, 2]}

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], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.20.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.40.2t1.b', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.760.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.152.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.760.6t1.b', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.380.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.380.6t1.b', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.152.6t1.b', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.14440.3t2.a', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.57760.6t3.d', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3040.12t18.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [2, 2], [0, -2], [1, 0], [-1, -1], [0, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.3040.12t18.d', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, -2], [2, 2], [1, 0], [0, 1], [-1, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.760.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.760.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [-1, 0], [1, 1], [0, -1], [0, 2], [-2, -2], [-1, 0], [0, -1], [1, 1], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]}, {'Size': '1', 'Order': 2, 'Representative': [3, 6, 1, 5, 4, 2, 10, 12, 17, 7, 15, 8, 16, 18, 11, 13, 9, 14]}, {'Size': '3', 'Order': 2, 'Representative': [3, 6, 1, 5, 4, 2, 16, 18, 11, 13, 9, 14, 10, 12, 17, 7, 15, 8]}, {'Size': '3', 'Order': 2, 'Representative': [13, 11, 16, 12, 8, 15, 7, 5, 9, 10, 2, 4, 1, 14, 6, 3, 17, 18]}, {'Size': '1', 'Order': 3, 'Representative': [5, 3, 4, 2, 6, 1, 14, 15, 7, 18, 16, 11, 8, 9, 13, 12, 10, 17]}, {'Size': '1', 'Order': 3, 'Representative': [6, 4, 2, 3, 1, 5, 9, 13, 14, 17, 12, 16, 15, 7, 8, 11, 18, 10]}, {'Size': '2', 'Order': 3, 'Representative': [7, 17, 10, 18, 14, 9, 13, 5, 15, 16, 2, 4, 1, 8, 6, 3, 11, 12]}, {'Size': '2', 'Order': 3, 'Representative': [14, 10, 18, 17, 9, 7, 8, 6, 13, 12, 3, 2, 5, 15, 1, 4, 16, 11]}, {'Size': '2', 'Order': 3, 'Representative': [15, 12, 11, 16, 13, 8, 6, 7, 5, 2, 18, 10, 9, 1, 14, 17, 4, 3]}, {'Size': '1', 'Order': 6, 'Representative': [2, 5, 6, 1, 3, 4, 17, 16, 18, 9, 8, 13, 11, 10, 12, 15, 14, 7]}, {'Size': '1', 'Order': 6, 'Representative': [4, 1, 5, 6, 2, 3, 18, 11, 10, 14, 13, 15, 12, 17, 16, 8, 7, 9]}, {'Size': '2', 'Order': 6, 'Representative': [16, 15, 13, 8, 12, 11, 3, 18, 2, 1, 9, 14, 10, 4, 17, 7, 6, 5]}, {'Size': '2', 'Order': 6, 'Representative': [11, 8, 15, 13, 16, 12, 2, 10, 4, 6, 14, 7, 17, 3, 18, 9, 5, 1]}, {'Size': '2', 'Order': 6, 'Representative': [18, 7, 14, 9, 17, 10, 12, 2, 16, 8, 1, 6, 4, 11, 3, 5, 13, 15]}, {'Size': '3', 'Order': 6, 'Representative': [2, 5, 6, 1, 3, 4, 11, 10, 12, 15, 14, 7, 17, 16, 18, 9, 8, 13]}, {'Size': '3', 'Order': 6, 'Representative': [4, 1, 5, 6, 2, 3, 12, 17, 16, 8, 7, 9, 18, 11, 10, 14, 13, 15]}, {'Size': '3', 'Order': 6, 'Representative': [15, 12, 11, 16, 13, 8, 9, 1, 14, 17, 4, 3, 6, 7, 5, 2, 18, 10]}, {'Size': '3', 'Order': 6, 'Representative': [8, 16, 12, 11, 15, 13, 14, 6, 7, 18, 3, 2, 5, 9, 1, 4, 10, 17]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['6', '1'], 'ConjugacyClass': 2}, {'RootOf': ['3032', '2140', '-6', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['18', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-8', '1'], 'ConjugacyClass': 6}, {'RootOf': ['236', '-28', '1'], 'ConjugacyClass': 7}, {'RootOf': ['1316', '-68', '1'], 'ConjugacyClass': 8}, {'RootOf': ['364', '-4', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['74720', '2860', '-12', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-4472', '732', '-50', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [3, 3, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['8', '1'], 'ConjugacyClass': 10}, {'RootOf': ['18', '1'], 'ConjugacyClass': 11}, {'RootOf': ['676', '-12', '1'], 'ConjugacyClass': 12}, {'RootOf': ['2540', '100', '1'], 'ConjugacyClass': 13}, {'RootOf': ['1036', '52', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-166752', '1836', '108', '1'], 'ConjugacyClass': 15}, {'RootOf': ['34648', '2292', '70', '1'], 'ConjugacyClass': 16}], 'Algorithm': 'RES', 'CycleType': [6, 6, 6]}], 'Frobs': [6, 17, 10, 7, 12, 11, 15, 14, 8, 18, 3, 12, 9, 17, 5, 14, 10, 18, 18, 15, 15, 15, 4, 8, 15, 18, 7, 4, 17, 3, 8, 13, 16, 11, 17, 3, 13, 4, 8, 13, 12, 18, 3, 15, 12, 16, 13, 9, 4, 4, 15, 3, 5, 11, 16, 9, 17, 15, 2, 8, 17, 12, 17, 3, 16, 14, 12, 15, 17, 4, 3, 15, 5, 12, 2, 6, 18, 13, 6, 8, 12, 17, 16, 16, 15, 18, 7, 3, 17, 7, 4, 16, 7, 13, 13, 8, 18, 1, 18, 18, 18, 14, 4, 7, 2, 3, 17, 16, 16, 7, 7, 13, 16, 12, 16, 6, 17, 7, 12, 14, 18, 3, 12, 4, 12, 17, 18, 15, 6, 12, 13, 9, 16, 13, 7, 5, 14, 4, 12, 1, 14, 18, 8, 18, 4, 15, 10, 15, 14, 7, 13, 7, 18, 5, 17, 3, 3, 9, 16, 18, 17, 15, 6, 10, 3, 9, 15, 14], 'G-Gens': [[2, 5, 6, 1, 3, 4, 11, 10, 12, 15, 14, 7, 17, 16, 18, 9, 8, 13], [13, 11, 16, 12, 8, 15, 7, 5, 9, 10, 2, 4, 1, 14, 6, 3, 17, 18], [16, 15, 13, 8, 12, 11, 3, 18, 2, 1, 9, 14, 10, 4, 17, 7, 6, 5], [1, 2, 3, 4, 5, 6, 13, 14, 15, 16, 17, 18, 7, 8, 9, 10, 11, 12]], 'G-Name': 'C6*S3', 'Polynomial': [68921, -127756, 97785, -58082, 39442, -10038, -13003, 2468, 7265, -232, -1417, -978, 431, 90, 42, -26, -2, -2, 1], 'QpRts': [['1144984993', '961940038', '-809245208', '4237271101', '6468480322', '-8367544686'], ['-1783386620', '-6691626872', '-2379917607', '-3464870198', '-2940729973', '-7228331389'], ['1686485782', '4341497531', '3463318981', '-6390966236', '-6827082969', '-4388230757'], ['7253438449', '2350129341', '-1083401374', '-7394039875', '-7482063367', '-5633314163'], ['1558484225', '-5412282898', '-468691802', '5910243729', '4268120651', '6798165996'], ['7777358754', '4450342860', '1277937010', '7102361479', '6513275336', '1569378690'], ['-4676388061', '7624527259', '505295306', '-2393393644', '-2936970428', '7251655451'], ['6832644525', '4626390447', '-8429674418', '-2745525257', '6479123932', '7383018932'], ['2927153500', '-855186966', '-634136794', '1551856224', '7356543429', '-1442079030'], ['108593708', '2230235394', '5647275743', '-6027670080', '-2851385335', '-4514905523'], ['4309675709', '-2960016578', '-1041723553', '1240414495', '6496623830', '4722503464'], ['7275199222', '-7353027970', '-1201680107', '-1069993797', '-6440096760', '-2922853878'], ['-1429219433', '3462365780', '4392686038', '-3498759050', '-4672734169', '-1984487363'], ['50607346', '-1933395897', '7394103736', '7157238308', '4236532209', '3837890620'], ['-574252152', '4325175686', '-3228273868', '-71416581', '6787381336', '2203877699'], ['7169883957', '5477100152', '-5021858588', '-6486121586', '8537244029', '5802759682'], ['4279680652', '322098721', '837167508', '-6442619484', '-148570065', '4837005284'], ['7838684373', '2283610281', '780818997', '1536114143', '-5593815699', '-7924509029']], 'QpRts-minpoly': [2, 13, 17, 25, 1, 0, 1], 'QpRts-p': 29, 'QpRts-prec': 7, 'Size': 36, 'TransitiveDegree': 18}

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Elliptic curves over $\Q$
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Genus 2 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.