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ec_curvedata • Show schema
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{'Ciso': '33282y', 'Clabel': '33282y1', 'Cnumber': 1, 'abc_quality': 0.8541295359409509, 'absD': 136331168037938064, 'adelic_genus': 2, 'adelic_index': 96, 'adelic_level': 516, 'ainvs': [1, -1, 1, -283244, -55164193], 'analytic_rank': 1, 'bad_primes': [2, 3, 43], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 33282, 'degree': 433440, 'elladic_images': ['2.2.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0438299195726534805441650388', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'intrinsic_torsion': 1, 'iso_nlabel': 18, 'isogeny_degrees': [1, 3], 'jinv': [294937, 16], 'lmfdb_iso': '33282.s', 'lmfdb_label': '33282.s2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -17, -33], 'min_quad_twist_disc': 129, 'modell_images': ['2Cn', '3B.1.2'], 'modm_images': ['2.2.0.a.1', '3.8.0-3.a.1.1', '6.16.0-6.a.1.1', '12.32.0-12.a.2.1', '86.6.0.?', '258.48.0.?', '516.96.2.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.3966785793088360617865248437', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 4, 16641], [3, 2, 3698], [43, 674, 18]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0129429685571096474686859219', 'prec': 103}, 'szpiro_ratio': 4.732245338845808, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 0, 1, -3, 0, -1, 1, 0, -3, 0, 0, -1, -1, 0, 1, -3, 0, -7, -3], 'aplist': [1, 0, -3, -1, 0, -1, -3, -7, 3, 9, -7, 11, -6, 0, 0, 9, 12, -1, 5, -3, 11, -1, 15, 9, -10], 'class_deg': 3, 'class_size': 2, 'conductor': 33282, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '33282.s', 'trace_hash': 2022116495914867521}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.016778451928441149830784183838', 'prec': 107}, 'conductor': 33282, 'gens': [[-2309, 23789, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '2.3966785793088360617865248437', 'prec': 100}], 'lmfdb_label': '33282.s2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.20764635241911063661887528258', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.9719387789739516968915961022523564716', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 0], '3': 'a', '5': [1, 0], '7': [1, 0], '11': [3, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [3, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': 'a', '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '33282.s2'}
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ec_torsion_growth • Show schema
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id: 1653496
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '33282.s2', 'torsion': [3]}
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id: 1653497
{'degree': 3, 'field': [-8, -14, -1, 1], 'lmfdb_label': '33282.s2', 'torsion': [2, 2]}
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id: 1653498
{'degree': 3, 'field': [121, 29, -1, 1], 'lmfdb_label': '33282.s2', 'torsion': [3]}
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id: 1653500
{'degree': 6, 'field': [64, 112, 188, 30, 15, -1, 1], 'lmfdb_label': '33282.s2', 'torsion': [2, 6]}
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id: 1653499
{'degree': 6, 'field': [1083, 57, -56, -3, 4, -3, 1], 'lmfdb_label': '33282.s2', 'torsion': [3, 3]}
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id: 1653501
{'degree': 9, 'field': [-64, 0, 0, -124, 0, 0, -12, 0, 0, 1], 'lmfdb_label': '33282.s2', 'torsion': [2, 6]}
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id: 1653502
{'degree': 12, 'field': [-428, 1536, -1311, 935, 253, -116, 138, 46, -34, 4, 5, -5, 1], 'lmfdb_label': '33282.s2', 'torsion': [2, 4]}
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id: 1653503
{'degree': 18, 'field': [1, -9, 54, -109, 15, 87, 666, -2352, 4407, -5403, 4704, -2667, 1064, -303, 183, -92, 9, 0, 1], 'lmfdb_label': '33282.s2', 'torsion': [9]}
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id: 1653504
{'degree': 18, 'field': [3267, -14553, 36657, -67032, 93006, -78474, 39154, -14568, 10269, -7983, 5055, -1824, 382, -210, 198, -108, 39, -9, 1], 'lmfdb_label': '33282.s2', 'torsion': [6, 6]}
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ec_localdata • Show schema
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id: 778958
{'conductor': 33282, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '33282.s2', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 778959
{'conductor': 33282, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '33282.s2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 778960
{'conductor': 33282, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '33282.s2', 'prime': 43, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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id: 1886282
{'adelic_gens': [[480, 511, 425, 47], [163, 514, 114, 503], [259, 12, 6, 73], [7, 12, 450, 403], [5, 2, 478, 501], [1, 0, 12, 1], [1, 12, 0, 1], [505, 12, 504, 13]], 'adelic_image': '516.96.2.?', 'conductor': 33282, 'lmfdb_label': '33282.s2', 'prime': 0}
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id: 148363
{'conductor': 33282, 'elladic_image': '2.2.0.1', 'lmfdb_label': '33282.s2', 'modell_image': '2Cn', 'prime': 2}
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id: 148364
{'conductor': 33282, 'elladic_image': '3.8.0.2', 'lmfdb_label': '33282.s2', 'modell_image': '3B.1.2', 'prime': 3}
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ec_padic • Show schema
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id: 1623659
{'lmfdb_iso': '33282.s', 'p': 5, 'prec': 20, 'unit': 14335338424014, 'val': 1}
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id: 1623660
{'lmfdb_iso': '33282.s', 'p': 7, 'prec': 20, 'unit': 6386428835891012, 'val': 1}
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id: 1623665
{'lmfdb_iso': '33282.s', 'p': 13, 'prec': 20, 'unit': 1411357890701825901870, 'val': 1}
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id: 1623667
{'lmfdb_iso': '33282.s', 'p': 17, 'prec': 20, 'unit': 54173929941049231641210, 'val': 1}
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id: 1623656
{'lmfdb_iso': '33282.s', 'p': 19, 'prec': 20, 'unit': 579478615256403878070445, 'val': 1}
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id: 1623671
{'lmfdb_iso': '33282.s', 'p': 23, 'prec': 20, 'unit': 2204962415181297807566696, 'val': 1}
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id: 1623664
{'lmfdb_iso': '33282.s', 'p': 29, 'prec': 20, 'unit': 49744639956720492398402440, 'val': 2}
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id: 1623661
{'lmfdb_iso': '33282.s', 'p': 31, 'prec': 20, 'unit': 3485055153207731489156206323, 'val': 1}
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id: 1623675
{'lmfdb_iso': '33282.s', 'p': 37, 'prec': 20, 'unit': 256588143598318619192477152378, 'val': 1}
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id: 1623662
{'lmfdb_iso': '33282.s', 'p': 41, 'prec': 20, 'unit': 1380573936867565584279366905754, 'val': 1}
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id: 1623669
{'lmfdb_iso': '33282.s', 'p': 53, 'prec': 20, 'unit': 224073005099820328803987562777335, 'val': 1}
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id: 1623673
{'lmfdb_iso': '33282.s', 'p': 59, 'prec': 20, 'unit': 115734657157892945741842506376180, 'val': 1}
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id: 1623674
{'lmfdb_iso': '33282.s', 'p': 61, 'prec': 20, 'unit': 1751099612568680057530340663590004, 'val': 1}
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id: 1623658
{'lmfdb_iso': '33282.s', 'p': 67, 'prec': 20, 'unit': 5527480706662040383433767915064206, 'val': 1}
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id: 1623663
{'lmfdb_iso': '33282.s', 'p': 71, 'prec': 20, 'unit': 115020264625821665514398002684181664, 'val': 1}
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id: 1623670
{'lmfdb_iso': '33282.s', 'p': 73, 'prec': 20, 'unit': 104702858855954832856568873397142073, 'val': 1}
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id: 1623666
{'lmfdb_iso': '33282.s', 'p': 79, 'prec': 20, 'unit': 519585805136051443755856666470134986, 'val': 1}
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id: 1623668
{'lmfdb_iso': '33282.s', 'p': 83, 'prec': 20, 'unit': 819339295180440434865487598571475392, 'val': 1}
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id: 1623672
{'lmfdb_iso': '33282.s', 'p': 89, 'prec': 20, 'unit': 2719893280401036584867148147784552269, 'val': 1}
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id: 1623657
{'lmfdb_iso': '33282.s', 'p': 97, 'prec': 20, 'unit': 3876155309014160728455753483821209427, 'val': 1}