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ec_curvedata • Show schema
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{'Ciso': '31850be', 'Clabel': '31850be1', 'Cnumber': 1, 'abc_quality': 0.945239209920167, 'absD': 10023318323200, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 5460, 'ainvs': [1, 0, 1, -6396, 248378], 'analytic_rank': 1, 'bad_primes': [2, 5, 7, 13], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 31850, 'degree': 84240, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.2060345051724501940805271168', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 3], 'jinv': [-9836106385, 3407872], 'lmfdb_iso': '31850.e', 'lmfdb_label': '31850.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -130, -780], 'min_quad_twist_disc': -7, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '52.2.0.a.1', '105.8.0.?', '156.8.0.?', '5460.16.0.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.7898058615636857111352466040', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.035160221427556520905609143793', 'prec': 110}, 'szpiro_ratio': 3.7008019968289285, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -2, 1, 0, 2, 0, -1, 1, 0, -3, -2, 1, 0, 0, 1, 3, -1, 4, 0], 'aplist': [-1, -2, 0, 0, -3, 1, 3, 4, -6, 9, -5, -2, 0, -2, -9, 9, 9, 1, -5, 0, 14, -16, -15, 6, 8], 'class_deg': 3, 'class_size': 2, 'conductor': 31850, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '31850.e', 'trace_hash': 2153579209978761551}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.089629657906960662425702647387', 'prec': 107}, 'conductor': 31850, 'gens': [[-79, 551, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.7898058615636857111352466040', 'prec': 100}], 'lmfdb_label': '31850.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.68328582269071860418498082714', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4458979411504268058881350982853514086', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': [-79]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 0], '3': [5, 0], '5': 'a', '7': 'a', '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '31850.e2'}
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ec_torsion_growth • Show schema
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id: 1587289
{'degree': 2, 'field': [9, -1, 1], 'lmfdb_label': '31850.e2', 'torsion': [3]}
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id: 1587290
{'degree': 3, 'field': [-13, -3, -1, 1], 'lmfdb_label': '31850.e2', 'torsion': [2]}
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id: 1587291
{'degree': 6, 'field': [36, 48, 41, 22, 6, -2, 1], 'lmfdb_label': '31850.e2', 'torsion': [2, 2]}
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id: 1587292
{'degree': 6, 'field': [156, -156, -455, -235, -30, -1, 1], 'lmfdb_label': '31850.e2', 'torsion': [3]}
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id: 1587293
{'degree': 6, 'field': [639, -672, 160, 50, -20, -2, 1], 'lmfdb_label': '31850.e2', 'torsion': [6]}
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id: 1587294
{'degree': 12, 'field': [-845221, -520532, -1056438, -557560, -212070, -113322, -39834, -616, -1010, 100, 12, -6, 1], 'lmfdb_label': '31850.e2', 'torsion': [4]}
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id: 1587295
{'degree': 12, 'field': [374544, 341496, 241488, 125550, 24975, -21789, 5259, -1608, -20, -30, 13, -3, 1], 'lmfdb_label': '31850.e2', 'torsion': [3, 3]}
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id: 1587296
{'degree': 12, 'field': [544644, 0, -14328, 0, -28235, 0, 4770, 0, -145, 0, -18, 0, 1], 'lmfdb_label': '31850.e2', 'torsion': [2, 6]}
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id: 1587298
{'degree': 18, 'field': [-12222080, -23335520, -65720720, -89597560, -79266460, -51316980, -24409866, -8179834, -1513577, 178515, 223510, 80081, 12759, 662, -465, -45, -22, -3, 1], 'lmfdb_label': '31850.e2', 'torsion': [6]}
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id: 1587297
{'degree': 18, 'field': [537616, -1788168, 1932336, 1035074, -1032165, -653898, 543634, 110562, -96477, -44060, 26871, 4362, -2909, -1056, 435, 84, -12, -6, 1], 'lmfdb_label': '31850.e2', 'torsion': [9]}
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ec_localdata • Show schema
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id: 744105
{'conductor': 31850, 'conductor_valuation': 1, 'discriminant_valuation': 18, 'j_denominator_valuation': 18, 'kodaira_symbol': 22, 'lmfdb_label': '31850.e2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 744106
{'conductor': 31850, 'conductor_valuation': 2, 'discriminant_valuation': 2, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '31850.e2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 744107
{'conductor': 31850, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '31850.e2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 744108
{'conductor': 31850, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '31850.e2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1876884
{'adelic_gens': [[4, 3, 9, 7], [3119, 0, 0, 5459], [5455, 6, 5454, 7], [2731, 3906, 1953, 799], [4201, 3906, 903, 799], [3186, 721, 5005, 4551], [1, 6, 0, 1], [3, 4, 8, 11], [2031, 3122, 4690, 3907], [1, 0, 6, 1]], 'adelic_image': '5460.16.0.?', 'conductor': 31850, 'lmfdb_label': '31850.e2', 'prime': 0}
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id: 142491
{'conductor': 31850, 'elladic_image': '3.4.0.1', 'lmfdb_label': '31850.e2', 'modell_image': '3B', 'prime': 3}
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ec_padic • Show schema
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id: 1550131
{'lmfdb_iso': '31850.e', 'p': 11, 'prec': 20, 'unit': 49757411115553503940, 'val': 1}
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id: 1550132
{'lmfdb_iso': '31850.e', 'p': 17, 'prec': 20, 'unit': 171283626646076519636243, 'val': 1}
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id: 1550133
{'lmfdb_iso': '31850.e', 'p': 19, 'prec': 20, 'unit': 442676315827114385053922, 'val': 1}
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id: 1550136
{'lmfdb_iso': '31850.e', 'p': 23, 'prec': 20, 'unit': 4012074663218250384962255, 'val': 1}
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id: 1550129
{'lmfdb_iso': '31850.e', 'p': 29, 'prec': 20, 'unit': 5831977407422368556748488541, 'val': 1}
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id: 1550140
{'lmfdb_iso': '31850.e', 'p': 31, 'prec': 20, 'unit': 1895073780512226202100354369, 'val': 1}
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id: 1550126
{'lmfdb_iso': '31850.e', 'p': 37, 'prec': 20, 'unit': 77938042779381473482625812649, 'val': 1}
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id: 1550128
{'lmfdb_iso': '31850.e', 'p': 43, 'prec': 20, 'unit': 663696977216493389508489911755, 'val': 1}
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id: 1550138
{'lmfdb_iso': '31850.e', 'p': 47, 'prec': 20, 'unit': 17649542561139342676489566583637, 'val': 1}
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id: 1550134
{'lmfdb_iso': '31850.e', 'p': 53, 'prec': 20, 'unit': 567561575323938736567192889833476, 'val': 1}
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id: 1550135
{'lmfdb_iso': '31850.e', 'p': 59, 'prec': 20, 'unit': 3512988048720591538510423807685287, 'val': 1}
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id: 1550139
{'lmfdb_iso': '31850.e', 'p': 61, 'prec': 20, 'unit': 169763702471835293393685772441967583, 'val': -1}
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id: 1550125
{'lmfdb_iso': '31850.e', 'p': 67, 'prec': 20, 'unit': 32888068586845441161232921695231066, 'val': 1}
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id: 1550127
{'lmfdb_iso': '31850.e', 'p': 73, 'prec': 20, 'unit': 78644697573901296361287159470550193, 'val': 1}
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id: 1550130
{'lmfdb_iso': '31850.e', 'p': 79, 'prec': 20, 'unit': 489396530148192133454809957552034604, 'val': 1}
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id: 1550124
{'lmfdb_iso': '31850.e', 'p': 83, 'prec': 20, 'unit': 2865769467009205127124652191501874123, 'val': 1}
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id: 1550137
{'lmfdb_iso': '31850.e', 'p': 89, 'prec': 20, 'unit': 1813820833201385251754286572088933378, 'val': 1}
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id: 1550123
{'lmfdb_iso': '31850.e', 'p': 97, 'prec': 20, 'unit': 17808791729595165094659439100599967220, 'val': 1}