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ec_curvedata • Show schema
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{'Ciso': '120b', 'Clabel': '120b2', 'Cnumber': 2, 'abc_quality': 1.1324456905360707, 'absD': 230400, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 1, 0, -16, -16], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 120, 'degree': 16, 'elladic_images': ['8.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.27717050546999455497449051860', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [470596, 225], 'lmfdb_iso': '120.a', 'lmfdb_label': '120.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -16, -16], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0-2.a.1.1', '12.12.0-2.a.1.1', '20.12.0-2.a.1.1', '24.24.0-24.b.1.2', '40.24.0-40.a.1.3', '60.24.0-60.b.1.3', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 40], [5, 6, 24]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.85479315593661564615551728648', 'prec': 107}, 'szpiro_ratio': 4.176138181584208, '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, 1, 0, -1, 0, 4, 0, 1, 0, 0, 0, -6, 0, -1, 0, -2, 0, 4, 0], 'aplist': [0, 1, -1, 4, 0, -6, -2, 4, -8, -6, 0, -6, 10, -4, 8, 10, 0, 6, -4, 0, -14, 16, 12, 2, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 120, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '120.a', 'trace_hash': 2081987281515763739}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.7407934428722325545479195511', 'prec': 100}, 'conductor': 120, 'gens': [], 'heights': [], 'lmfdb_label': '120.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '2.4898202910989828059362675103', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2449101455494914029681337551638236476', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-1, 0, 1], [4, 0, 1]], 'xcoord_integral_points': [-4, -1, 4]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '5': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '120.a3'}
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ec_torsion_growth • Show schema
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id: 4581
{'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '120.a3', 'torsion': [2, 4]}
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id: 4583
{'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '120.a3', 'torsion': [2, 4]}
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id: 4582
{'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '120.a3', 'torsion': [2, 4]}
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id: 4584
{'degree': 8, 'field': [-48, 0, -16, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '120.a3', 'torsion': [2, 6]}
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id: 4586
{'degree': 16, 'field': [1, 0, -12, 0, -12, 0, -24, 0, 175, 0, -24, 0, -12, 0, -12, 0, 1], 'lmfdb_label': '120.a3', 'torsion': [2, 8]}
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id: 4585
{'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 48, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '120.a3', 'torsion': [4, 4]}
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id: 4588
{'degree': 16, 'field': [1, 0, 4, 0, 16, 0, -8, 0, -17, 0, -8, 0, 16, 0, 4, 0, 1], 'lmfdb_label': '120.a3', 'torsion': [2, 8]}
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id: 4587
{'degree': 16, 'field': [36, 0, 0, 0, 84, 0, 180, 0, 301, 0, -130, 0, 39, 0, -10, 0, 1], 'lmfdb_label': '120.a3', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 820
{'conductor': 120, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '120.a3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 821
{'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '120.a3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 822
{'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '120.a3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1666246
{'adelic_gens': [[41, 4, 82, 9], [31, 4, 62, 9], [117, 4, 116, 5], [97, 2, 0, 1], [63, 2, 118, 119], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '120.48.0.?', 'conductor': 120, 'lmfdb_label': '120.a3', 'prime': 0}
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id: 434
{'conductor': 120, 'elladic_image': '8.12.0.1', 'lmfdb_label': '120.a3', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 120.a does not appear in ec_padic
