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ec_curvedata • Show schema
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{'Ciso': '405d', 'Clabel': '405d2', 'Cnumber': 2, 'abc_quality': 1.0070302306950922, 'absD': 4613203125, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 1260, 'ainvs': [1, -1, 1, -2027, 35776], 'analytic_rank': 1, 'bad_primes': [3, 5], 'class_deg': 7, 'class_size': 2, 'cm': 0, 'conductor': 405, 'degree': 252, 'elladic_images': ['7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.70167136058330600768411451754', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 7, 'iso_nlabel': 1, 'isogeny_degrees': [1, 7], 'jinv': [-15590912409, 78125], 'lmfdb_iso': '405.b', 'lmfdb_label': '405.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -2027, 35776], 'min_quad_twist_disc': 1, 'modell_images': ['7B'], 'modm_images': ['7.8.0.a.1', '20.2.0.a.1', '21.16.0-7.a.1.1', '63.48.0-63.b.1.3', '140.16.0.?', '420.32.0.?', '1260.96.2.?'], 'nonmax_primes': [7], 'nonmax_rad': 7, 'num_bad_primes': 2, 'num_int_pts': 12, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.043718464769708359029862235393', 'prec': 107}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.21383887997345206847858984656', 'prec': 107}, 'szpiro_ratio': 5.740397539484409, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, -1, 1, 0, -3, 3, 0, -1, 2, 0, -2, 3, 0, -1, -4, 0, -8, -1], 'aplist': [-1, 0, 1, -3, 2, -2, -4, -8, -3, 1, 0, -4, -5, -8, -7, 2, 14, 7, -3, -2, 4, -6, -9, 15, 2], 'class_deg': 7, 'class_size': 2, 'conductor': 405, 'isogeny_matrix': [[1, 7], [7, 1]], 'lmfdb_iso': '405.b', 'trace_hash': 1346866818062352446}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.24577403522750112234210393516', 'prec': 103}, 'conductor': 405, 'gens': [[76, 524, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.043718464769708359029862235393', 'prec': 107}], 'lmfdb_label': '405.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.3820485347634765158428338742', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2688418437187662336679690472441060102', 'prec': 130}, 'tamagawa_product': 21, 'torsion_generators': [], 'xcoord_integral_points': [-49, -14, 4, 26, 31, 76]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 0], '3': 'a', '5': [2, 0], '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [3, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '405.b1'}
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ec_torsion_growth • Show schema
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id: 17767
{'degree': 3, 'field': [-8, -3, 0, 1], 'lmfdb_label': '405.b1', 'torsion': [2]}
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id: 17769
{'degree': 6, 'field': [-35, 21, 63, -14, -21, 0, 1], 'lmfdb_label': '405.b1', 'torsion': [7]}
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id: 17768
{'degree': 6, 'field': [80, 0, 36, 0, 12, 0, 1], 'lmfdb_label': '405.b1', 'torsion': [2, 2]}
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id: 17770
{'degree': 8, 'field': [-1, 4, -4, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '405.b1', 'torsion': [3]}
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id: 17771
{'degree': 12, 'field': [-494, -1086, -738, 44, 627, 525, 344, 27, -42, -11, 6, -3, 1], 'lmfdb_label': '405.b1', 'torsion': [4]}
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id: 17772
{'degree': 18, 'field': [40195, 703470, 2384316, 3188659, 1898028, 219924, -327440, -97512, 73800, 34919, -15348, -14040, -1568, 1362, 396, -57, -30, 0, 1], 'lmfdb_label': '405.b1', 'torsion': [14]}
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ec_localdata • Show schema
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id: 4179
{'conductor': 405, 'conductor_valuation': 4, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '405.b1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
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id: 4180
{'conductor': 405, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '405.b1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 7}
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ec_galrep • Show schema
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id: 1667541
{'adelic_gens': [[1016, 7, 1001, 1254], [8, 7, 623, 1254], [8, 5, 91, 57], [633, 1088, 1246, 953], [1247, 14, 1246, 15], [1, 14, 0, 1], [1, 0, 14, 1], [1251, 1250, 182, 1151]], 'adelic_image': '1260.96.2.?', 'conductor': 405, 'lmfdb_label': '405.b1', 'prime': 0}
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id: 1743
{'conductor': 405, 'elladic_image': '7.8.0.1', 'lmfdb_label': '405.b1', 'modell_image': '7B', 'prime': 7}
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ec_padic • Show schema
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id: 5344
{'lmfdb_iso': '405.b', 'p': 7, 'prec': 20, 'unit': 7403774212214235, 'val': 1}
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id: 5342
{'lmfdb_iso': '405.b', 'p': 11, 'prec': 20, 'unit': 46151583998976251974, 'val': 1}
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id: 5348
{'lmfdb_iso': '405.b', 'p': 13, 'prec': 20, 'unit': 212201179628710050634, 'val': 1}
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id: 5350
{'lmfdb_iso': '405.b', 'p': 17, 'prec': 20, 'unit': 5001309521022499058865, 'val': 2}
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id: 5351
{'lmfdb_iso': '405.b', 'p': 19, 'prec': 20, 'unit': 1684079045232333970996972, 'val': 1}
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id: 5355
{'lmfdb_iso': '405.b', 'p': 23, 'prec': 20, 'unit': 68747639946075238469303818, 'val': 1}
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id: 5347
{'lmfdb_iso': '405.b', 'p': 29, 'prec': 20, 'unit': 134557786871363497000491394022, 'val': -1}
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id: 5343
{'lmfdb_iso': '405.b', 'p': 37, 'prec': 20, 'unit': 20908870877297231631076205068, 'val': 1}
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id: 5345
{'lmfdb_iso': '405.b', 'p': 41, 'prec': 20, 'unit': 2759837963838572186177370604234, 'val': 1}
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id: 5346
{'lmfdb_iso': '405.b', 'p': 43, 'prec': 20, 'unit': 5381157676673697122943520286077, 'val': 1}
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id: 5358
{'lmfdb_iso': '405.b', 'p': 47, 'prec': 20, 'unit': 35117176481862058040668726875246, 'val': 1}
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id: 5352
{'lmfdb_iso': '405.b', 'p': 53, 'prec': 20, 'unit': 56649167877726912621537881967300, 'val': 1}
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id: 5353
{'lmfdb_iso': '405.b', 'p': 59, 'prec': 20, 'unit': 1686333347606286783219358783314588, 'val': 1}
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id: 5359
{'lmfdb_iso': '405.b', 'p': 61, 'prec': 20, 'unit': 8316057464701497057464047155063320, 'val': 1}
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id: 5341
{'lmfdb_iso': '405.b', 'p': 67, 'prec': 20, 'unit': 35047278335464214420839625539337097, 'val': 1}
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id: 5357
{'lmfdb_iso': '405.b', 'p': 71, 'prec': 20, 'unit': 113059354796967208241611812349270953, 'val': 1}
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id: 5354
{'lmfdb_iso': '405.b', 'p': 73, 'prec': 20, 'unit': 209368406975864094501232097865450746, 'val': 1}
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id: 5349
{'lmfdb_iso': '405.b', 'p': 79, 'prec': 20, 'unit': 186922571687578423639495750406188889, 'val': 1}
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id: 5360
{'lmfdb_iso': '405.b', 'p': 83, 'prec': 20, 'unit': 1458017434784957580990344322583065321, 'val': 1}
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id: 5356
{'lmfdb_iso': '405.b', 'p': 89, 'prec': 20, 'unit': 9047782880973893963722774018256024621, 'val': 1}
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id: 5340
{'lmfdb_iso': '405.b', 'p': 97, 'prec': 20, 'unit': 29264198002131063933784146775307699775, 'val': 1}