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ec_curvedata • Show schema
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{'Ciso': '57b', 'Clabel': '57b2', 'Cnumber': 2, 'abc_quality': 0.9626725733934746, 'absD': 57, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 456, 'ainvs': [1, 0, 1, -2, -1], 'analytic_rank': 0, 'bad_primes': [3, 19], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 57, 'degree': 6, 'elladic_images': ['8.12.0.6'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.93815584276277140308666449133', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 2, 'isogeny_degrees': [1, 2, 4], 'jinv': [389017, 57], 'lmfdb_iso': '57.c', 'lmfdb_label': '57.c3', 'lmfdb_number': 3, 'manin_constant': 2, 'min_quad_twist_ainvs': [1, 0, 1, -2, -1], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.5', '12.12.0-4.c.1.2', '24.24.0-24.z.1.4', '76.12.0.?', '114.6.0.?', '152.24.0.?', '228.24.0.?', '456.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.93815584276277140308666449133', 'prec': 107}, 'szpiro_ratio': 3.1835802889383236, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 1, -1, -2, 1, 0, -3, 1, -2, 0, -1, 6, 0, -2, -1, -6, 1, -1, 2], 'aplist': [1, 1, -2, 0, 0, 6, -6, -1, 4, 2, 8, -10, -2, -4, 12, -6, -12, -2, -4, 0, 10, 0, 16, -2, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 57, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '57.c', 'trace_hash': 75089547396961172}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '6.5293779964347407062112571440', 'prec': 100}, 'conductor': 57, 'gens': [], 'heights': [], 'lmfdb_label': '57.c3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '4.3412090890706928922224104326', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0853022722676732230556026081559242659', 'prec': 130}, 'tamagawa_product': 1, 'torsion_generators': [[-1, 0, 1]], 'xcoord_integral_points': [-1]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 0], '3': [3, 0], '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '57.c3'}
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ec_torsion_growth • Show schema
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id: 2017
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '57.c3', 'torsion': [2, 2]}
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id: 2018
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '57.c3', 'torsion': [4]}
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id: 2019
{'degree': 2, 'field': [5, -1, 1], 'lmfdb_label': '57.c3', 'torsion': [4]}
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id: 2021
{'degree': 4, 'field': [4, 2, -3, -1, 1], 'lmfdb_label': '57.c3', 'torsion': [8]}
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id: 2020
{'degree': 4, 'field': [25, -5, -4, -1, 1], 'lmfdb_label': '57.c3', 'torsion': [2, 4]}
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id: 2022
{'degree': 8, 'field': [-354, -534, -27, 168, 112, -14, -18, -2, 1], 'lmfdb_label': '57.c3', 'torsion': [2, 4]}
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id: 2025
{'degree': 8, 'field': [-3, 0, 11, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '57.c3', 'torsion': [6]}
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id: 2024
{'degree': 8, 'field': [1, -3, 1, 6, 6, 6, 1, -3, 1], 'lmfdb_label': '57.c3', 'torsion': [2, 8]}
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id: 2023
{'degree': 8, 'field': [36, 0, -32, 0, 93, 0, -18, 0, 1], 'lmfdb_label': '57.c3', 'torsion': [8]}
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id: 2027
{'degree': 16, 'field': [1, 0, 15, 0, 181, 0, 630, 0, 1710, 0, 630, 0, 181, 0, 15, 0, 1], 'lmfdb_label': '57.c3', 'torsion': [2, 8]}
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id: 2028
{'degree': 16, 'field': [9, -72, 216, -324, 387, -612, 756, -468, 141, -96, 144, -144, 81, -24, 6, 0, 1], 'lmfdb_label': '57.c3', 'torsion': [16]}
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id: 2030
{'degree': 16, 'field': [9, 0, 33, 0, 103, 0, 66, 0, 39, 0, 22, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '57.c3', 'torsion': [12]}
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id: 2031
{'degree': 16, 'field': [361, 0, 266, 0, -977, 0, 387, 0, 1389, 0, 558, 0, 31, 0, 5, 0, 1], 'lmfdb_label': '57.c3', 'torsion': [12]}
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id: 2029
{'degree': 16, 'field': [31329, 0, -37137, 0, 13696, 0, -3525, 0, 111, 0, 52, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '57.c3', 'torsion': [2, 6]}
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id: 2026
{'degree': 16, 'field': [38416, 5488, 392, 24360, -5512, -4156, 7186, -2814, 313, 642, -440, 154, -13, -12, 8, -4, 1], 'lmfdb_label': '57.c3', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 292
{'conductor': 57, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57.c3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 293
{'conductor': 57, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '57.c3', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1666028
{'adelic_gens': [[7, 6, 450, 451], [65, 60, 62, 287], [388, 1, 407, 6], [1, 0, 8, 1], [449, 8, 448, 9], [403, 402, 298, 67], [160, 3, 157, 2], [1, 8, 0, 1], [1, 4, 4, 17]], 'adelic_image': '456.48.0.?', 'conductor': 57, 'lmfdb_label': '57.c3', 'prime': 0}
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id: 180
{'conductor': 57, 'elladic_image': '8.12.0.6', 'lmfdb_label': '57.c3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 57.c does not appear in ec_padic