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ec_curvedata • Show schema
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{'Ciso': '48960bn', 'Clabel': '48960bn1', 'Cnumber': 1, 'abc_quality': 0.9201382831476481, 'absD': 97418894400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 2040, 'ainvs': [0, 0, 0, -4323, -110428], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 48960, 'degree': 36864, 'elladic_images': ['4.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.92412064816448229868193042422', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 21, 'isogeny_degrees': [1, 2], 'jinv': [-191501383744, 2088025], 'lmfdb_iso': '48960.v', 'lmfdb_label': '48960.v2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -1921, 32079], 'min_quad_twist_disc': -24, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.a.1', '12.12.0-4.a.1.1', '20.12.0.d.1', '60.24.0-20.d.1.1', '680.24.0.?', '2040.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 9], [3, 6, 5440], [5, 6, 9792], [17, 18, 2880]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.028240913550454798275691745030', 'prec': 107}, 'szpiro_ratio': 3.4029265610178534, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0], 'aplist': [0, 0, -1, -2, 0, -2, -1, 0, -2, 6, -8, -10, 2, -2, 6, 2, -8, -2, 2, -8, 2, -4, -6, 6, 10], 'class_deg': 2, 'class_size': 2, 'conductor': 48960, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '48960.v', 'trace_hash': 253805738353434124}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.15751394320817671663749036196', 'prec': 103}, 'conductor': 48960, 'gens': [], 'heights': [], 'lmfdb_label': '48960.v2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.29419891897872771437881739483', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.58839783795745542875763478966412650308', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[76, 0, 1]], 'xcoord_integral_points': [76]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '17': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '48960.v2'}
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ec_torsion_growth • Show schema
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id: 2382648
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [2, 2]}
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id: 2382649
{'degree': 4, 'field': [-36, 0, -6, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [4]}
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id: 2382652
{'degree': 8, 'field': [-75, 0, 0, 0, -30, 0, 16, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [6]}
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id: 2382650
{'degree': 8, 'field': [25, 0, -20, 0, 11, 0, -4, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [2, 4]}
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id: 2382651
{'degree': 8, 'field': [81, 0, 0, 0, 27, 0, 0, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [2, 4]}
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id: 2382653
{'degree': 16, 'field': [1, 0, 0, 0, -3, 0, 0, 0, 8, 0, 0, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [4, 4]}
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id: 2382655
{'degree': 16, 'field': [90000, 0, -13824, 0, 86472, 0, -41328, 0, 12405, 0, -2280, 0, 298, 0, -24, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [2, 6]}
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id: 2382654
{'degree': 16, 'field': [923521, 0, 24103356, 0, -21434530, 0, 6381704, 0, -693261, 0, 17864, 0, -930, 0, -4, 0, 1], 'lmfdb_label': '48960.v2', 'torsion': [8]}
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ec_localdata • Show schema
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id: 1170317
{'conductor': 48960, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '48960.v2', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 1170318
{'conductor': 48960, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '48960.v2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 1170319
{'conductor': 48960, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '48960.v2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1170320
{'conductor': 48960, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '48960.v2', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1990256
{'adelic_gens': [[1019, 1356, 678, 671], [3, 8, 10, 27], [1, 0, 8, 1], [817, 1362, 0, 1], [1, 8, 0, 1], [5, 8, 48, 77], [679, 0, 0, 2039], [2033, 8, 2032, 9], [241, 684, 0, 1], [509, 1356, 255, 2039]], 'adelic_image': '2040.48.0.?', 'conductor': 48960, 'lmfdb_label': '48960.v2', 'prime': 0}
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id: 211153
{'conductor': 48960, 'elladic_image': '4.6.0.5', 'lmfdb_label': '48960.v2', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 48960.v does not appear in ec_padic