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ec_curvedata • Show schema
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{'Ciso': '4050f', 'Clabel': '4050f4', 'Cnumber': 4, 'abc_quality': 1.1259568215438134, 'absD': 1062882000000, 'adelic_genus': 21, 'adelic_index': 768, 'adelic_level': 2520, 'ainvs': [1, -1, 0, -242367, -45865459], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 21, 'class_size': 4, 'cm': 0, 'conductor': 4050, 'degree': 18144, 'elladic_images': ['8.2.0.1', '3.4.0.1', '7.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6233931794287452148288425358', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 21, 'iso_nlabel': 2, 'isogeny_degrees': [1, 3, 7, 21], 'jinv': [-189613868625, 128], 'lmfdb_iso': '4050.c', 'lmfdb_label': '4050.c1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -1077, 13877], 'min_quad_twist_disc': -15, 'modell_images': ['3B', '7B'], 'modm_images': ['3.4.0.a.1', '7.8.0.a.1', '8.2.0.a.1', '15.8.0-3.a.1.1', '21.64.1.a.4', '24.8.0.a.1', '35.16.0-7.a.1.2', '56.16.0.a.1', '63.192.5.e.1', '105.128.1.?', '120.16.0.?', '168.128.5.?', '280.32.0.?', '315.384.5.?', '504.384.21.?', '840.256.5.?', '2520.768.21.?'], 'nonmax_primes': [2, 3, 7], 'nonmax_rad': 42, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '11.373818091712466418533324825', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27993806545641466386678236774', 'prec': 107}, 'szpiro_ratio': 5.875927919245049, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, 1, 0, 0, -2, -1, 0, 0, -3, 0, -2, 2, 0, 1, 3, 0, -1, 0], 'aplist': [-1, 0, 0, -2, -3, -2, 3, -1, 6, 6, -4, 4, 9, 1, 6, -12, 3, 8, -5, -12, -11, -4, -12, 6, -5], 'class_deg': 21, 'class_size': 4, 'conductor': 4050, 'isogeny_matrix': [[1, 3, 21, 7], [3, 1, 7, 21], [21, 7, 1, 3], [7, 21, 3, 1]], 'lmfdb_iso': '4050.c', 'trace_hash': 882489139600859620}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.038899014656039250091254776773', 'prec': 107}, 'conductor': 4050, 'gens': [[332549, 152033422, 19]], 'heights': [{'__RealLiteral__': 0, 'data': '11.373818091712466418533324825', 'prec': 100}], 'lmfdb_label': '4050.c1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.10758484181002043139677052740', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.4473008403456683092661451675208027771', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [6, 0], '3': 'a', '5': 'a', '7': [1, 1], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4050.c1'}
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ec_torsion_growth • Show schema
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id: 211723
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '4050.c1', 'torsion': [3]}
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id: 211724
{'degree': 3, 'field': [-10, -3, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [2]}
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id: 211726
{'degree': 6, 'field': [-4, 0, 0, -8, 0, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [3]}
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id: 211725
{'degree': 6, 'field': [8, 0, 9, 0, -6, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [2, 2]}
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id: 211728
{'degree': 6, 'field': [96, -72, 36, -18, 3, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [6]}
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id: 211727
{'degree': 6, 'field': [2961, -2898, 756, -98, 42, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [7]}
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id: 211730
{'degree': 12, 'field': [1, 3, -9, -20, 45, 33, -70, -33, 45, 20, -9, -3, 1], 'lmfdb_label': '4050.c1', 'torsion': [3, 3]}
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id: 211731
{'degree': 12, 'field': [784, 0, 1656, 0, 1185, 0, 292, 0, 54, 0, 12, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [2, 6]}
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id: 211729
{'degree': 12, 'field': [6074, 2112, -14577, -15662, 2793, 5904, -555, -1074, 237, 40, -3, -6, 1], 'lmfdb_label': '4050.c1', 'torsion': [4]}
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id: 211732
{'degree': 12, 'field': [110544, -155232, 86436, -58800, 41601, -10584, 6874, -1512, 567, -56, 42, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [21]}
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id: 211734
{'degree': 18, 'field': [-64, 96, -288, 456, -912, 18, -963, 48, -117, -302, -474, -288, -333, -246, -54, -24, -9, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [6]}
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id: 211733
{'degree': 18, 'field': [2116, -7920, 24300, -25962, 19998, 11232, -11559, -20880, 2754, 9961, 2493, -2268, -975, 252, 189, -15, -18, 0, 1], 'lmfdb_label': '4050.c1', 'torsion': [9]}
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id: 211735
{'degree': 18, 'field': [1889057836, -2356486650, 2281167711, -1080394043, 400288212, -73632357, 18023483, 2700468, -19080, 728436, -34524, 84636, 3260, 3006, 1389, -77, 72, -3, 1], 'lmfdb_label': '4050.c1', 'torsion': [14]}
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ec_localdata • Show schema
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id: 75955
{'conductor': 4050, 'conductor_valuation': 1, 'discriminant_valuation': 7, 'j_denominator_valuation': 7, 'kodaira_symbol': 11, 'lmfdb_label': '4050.c1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 75956
{'conductor': 4050, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '4050.c1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 75957
{'conductor': 4050, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4050.c1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1690367
{'adelic_gens': [[1, 1680, 0, 1], [2101, 1050, 2205, 1051], [1, 720, 0, 1], [1081, 1410, 0, 1], [39, 1070, 560, 2319], [1, 0, 420, 1], [1471, 1290, 420, 2311], [2311, 1050, 735, 211], [503, 0, 0, 2519], [1, 0, 1680, 1], [1, 930, 1050, 1261], [1, 0, 1470, 1], [841, 1680, 840, 1681], [505, 2016, 504, 505], [281, 1400, 1120, 1401], [526, 825, 2205, 1681], [1, 0, 2016, 1]], 'adelic_image': '2520.768.21.?', 'conductor': 4050, 'lmfdb_label': '4050.c1', 'prime': 0}
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id: 20178
{'conductor': 4050, 'elladic_image': '8.2.0.1', 'lmfdb_label': '4050.c1', 'modell_image': '2G', 'prime': 2}
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id: 20179
{'conductor': 4050, 'elladic_image': '3.4.0.1', 'lmfdb_label': '4050.c1', 'modell_image': '3B', 'prime': 3}
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id: 20180
{'conductor': 4050, 'elladic_image': '7.8.0.1', 'lmfdb_label': '4050.c1', 'modell_image': '7B', 'prime': 7}
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ec_padic • Show schema
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id: 142060
{'lmfdb_iso': '4050.c', 'p': 7, 'prec': 20, 'unit': 157959337004146, 'val': 1}
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id: 142061
{'lmfdb_iso': '4050.c', 'p': 11, 'prec': 20, 'unit': 53165851172682463848, 'val': 1}
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id: 142062
{'lmfdb_iso': '4050.c', 'p': 13, 'prec': 20, 'unit': 1439300826685634456013, 'val': 1}
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id: 142063
{'lmfdb_iso': '4050.c', 'p': 17, 'prec': 20, 'unit': 121098448101760962209768, 'val': 1}
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id: 142064
{'lmfdb_iso': '4050.c', 'p': 19, 'prec': 20, 'unit': 454298560088067549603656, 'val': 1}
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id: 142065
{'lmfdb_iso': '4050.c', 'p': 23, 'prec': 20, 'unit': 40043137948829242542746637, 'val': 1}
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id: 142066
{'lmfdb_iso': '4050.c', 'p': 29, 'prec': 20, 'unit': 5665289711044395103616663088, 'val': 1}
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id: 142067
{'lmfdb_iso': '4050.c', 'p': 31, 'prec': 20, 'unit': 14831805391755899281207192097, 'val': 1}
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id: 142068
{'lmfdb_iso': '4050.c', 'p': 37, 'prec': 20, 'unit': 22822408535916808326611425660, 'val': 1}
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id: 142069
{'lmfdb_iso': '4050.c', 'p': 41, 'prec': 20, 'unit': 3274452512073392057008970563830, 'val': 1}
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id: 142070
{'lmfdb_iso': '4050.c', 'p': 43, 'prec': 20, 'unit': 131763876999797698311063857739478, 'val': -1}
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id: 142071
{'lmfdb_iso': '4050.c', 'p': 47, 'prec': 20, 'unit': 48399551129735591334156316651907, 'val': 1}
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id: 142072
{'lmfdb_iso': '4050.c', 'p': 53, 'prec': 20, 'unit': 112628206727292277481325612882478, 'val': 1}
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id: 142073
{'lmfdb_iso': '4050.c', 'p': 59, 'prec': 20, 'unit': 2367820750892833608891165225358144, 'val': 1}
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id: 142074
{'lmfdb_iso': '4050.c', 'p': 61, 'prec': 20, 'unit': 8020944553612111426540703436822256, 'val': 1}
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id: 142075
{'lmfdb_iso': '4050.c', 'p': 67, 'prec': 20, 'unit': 32290172084847927516194795226915720, 'val': 1}
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id: 142076
{'lmfdb_iso': '4050.c', 'p': 71, 'prec': 20, 'unit': 69251656818804709223791949080253040, 'val': 1}
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id: 142077
{'lmfdb_iso': '4050.c', 'p': 73, 'prec': 20, 'unit': 222493650370114839298901311719165372, 'val': 1}
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id: 142078
{'lmfdb_iso': '4050.c', 'p': 79, 'prec': 20, 'unit': 702051198738997526103432775357879101, 'val': 1}
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id: 142079
{'lmfdb_iso': '4050.c', 'p': 83, 'prec': 20, 'unit': 267202470410300694008735539755996988, 'val': 1}
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id: 142080
{'lmfdb_iso': '4050.c', 'p': 89, 'prec': 20, 'unit': 4723268865548556745883196818711838499, 'val': 1}
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id: 142081
{'lmfdb_iso': '4050.c', 'p': 97, 'prec': 20, 'unit': 118454727572941527993294258727623652, 'val': 2}