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ec_curvedata • Show schema
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{'Ciso': '56a', 'Clabel': '56a2', 'Cnumber': 2, 'abc_quality': 1.0653400939100561, 'absD': 50176, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 56, 'ainvs': [0, 0, 0, -19, 30], 'analytic_rank': 0, 'bad_primes': [2, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 56, 'degree': 4, 'elladic_images': ['8.24.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.34860641707856014305515959772', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [740772, 49], 'lmfdb_iso': '56.a', 'lmfdb_label': '56.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -19, 30], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '8.24.0-8.a.1.2', '28.24.0-28.b.1.1', '56.48.0-56.d.1.3'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.92622906754518123423618636560', 'prec': 107}, 'szpiro_ratio': 5.0795362843162595, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 2, 0, -1, 0, -3, 0, -4, 0, 2, 0, 0, 0, -6, 0, 8, 0], 'aplist': [0, 0, 2, -1, -4, 2, -6, 8, 0, 6, 8, -2, 2, -4, -8, 6, 0, -6, -4, -8, 10, 16, 8, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 56, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '56.a', 'trace_hash': 1158293942075606764}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '2.0081478591574363056148124429', 'prec': 100}, 'conductor': 56, 'gens': [], 'heights': [], 'lmfdb_label': '56.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.4981932567533454612034413989', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.87454831418833636530086034972735623668', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[2, 0, 1], [3, 0, 1]], 'xcoord_integral_points': [-5, 2, 3]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '56.a3'}
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ec_torsion_growth • Show schema
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id: 1951
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '56.a3', 'torsion': [2, 4]}
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id: 1953
{'degree': 4, 'field': [2, -8, 9, -2, 1], 'lmfdb_label': '56.a3', 'torsion': [2, 4]}
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id: 1952
{'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '56.a3', 'torsion': [2, 4]}
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id: 1956
{'degree': 8, 'field': [1, -4, 4, 2, -8, 2, 4, -4, 1], 'lmfdb_label': '56.a3', 'torsion': [2, 6]}
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id: 1955
{'degree': 8, 'field': [1, 0, -4, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '56.a3', 'torsion': [2, 8]}
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id: 1954
{'degree': 8, 'field': [16, 0, 0, 0, 1, 0, 0, 0, 1], 'lmfdb_label': '56.a3', 'torsion': [4, 4]}
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id: 1957
{'degree': 16, 'field': [1, 0, 0, 0, -3, 0, 0, 0, 20, 0, 0, 0, -3, 0, 0, 0, 1], 'lmfdb_label': '56.a3', 'torsion': [2, 8]}
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id: 1959
{'degree': 16, 'field': [64, 0, -256, 0, 256, 0, 128, 0, -176, 0, -40, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '56.a3', 'torsion': [2, 12]}
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id: 1958
{'degree': 16, 'field': [256, 0, -768, 0, 896, 0, 1680, 0, 1057, 0, 420, 0, 56, 0, -12, 0, 1], 'lmfdb_label': '56.a3', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 278
{'conductor': 56, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '56.a3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 279
{'conductor': 56, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '56.a3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1666019
{'adelic_gens': [[15, 4, 0, 1], [17, 4, 34, 9], [29, 2, 0, 1], [53, 4, 52, 5], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '56.48.0.?', 'conductor': 56, 'lmfdb_label': '56.a3', 'prime': 0}
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id: 172
{'conductor': 56, 'elladic_image': '8.24.0.1', 'lmfdb_label': '56.a3', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 56.a does not appear in ec_padic