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ec_curvedata • Show schema
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{'Ciso': '7056bq', 'Clabel': '7056bq1', 'Cnumber': 1, 'abc_quality': 0.9802957926219806, 'absD': 1024192512, 'ainvs': [0, 0, 0, -315, -2646], 'analytic_rank': 0, 'bad_primes': [2, 3, 7], 'class_deg': 14, 'class_size': 4, 'cm': -7, 'conductor': 7056, 'degree': 2048, 'elladic_images': [], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.44331493583837773799054303019', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 32, 'isogeny_degrees': [1, 2, 7, 14], 'jinv': [-3375, 1], 'lmfdb_iso': '7056.bg', 'lmfdb_label': '7056.bg4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -2, -1], 'min_quad_twist_disc': 12, 'modell_images': [], 'nonmax_primes': [], 'nonmax_rad': 1, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2856159263194507434006498956', 'prec': 103}, 'szpiro_ratio': 3.3046676895558895, '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, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'aplist': [0, 0, 0, 0, 4, 0, 0, 0, 8, -2, 0, -6, 0, 12, 0, 10, 0, 0, -4, 16, 0, -8, 0, 0, 0], 'class_deg': 14, 'class_size': 4, 'conductor': 7056, 'isogeny_matrix': [[1, 2, 7, 14], [2, 1, 14, 7], [7, 14, 1, 2], [14, 7, 2, 1]], 'lmfdb_iso': '7056.bg', 'trace_hash': 520392068974718912}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.41204205002354556137484974735', 'prec': 103}, 'conductor': 7056, 'gens': [], 'heights': [], 'lmfdb_label': '7056.bg4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.55809901683266033382036113112', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.2323960673306413352814445244990738053', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[21, 0, 1]], 'xcoord_integral_points': [21]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [0, 0, 0], '7': 'a'}, 'iwp0': 11, 'lmfdb_label': '7056.bg4'}
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ec_torsion_growth • Show schema
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id: 371412
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '7056.bg4', 'torsion': [2, 2]}
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id: 371413
{'degree': 4, 'field': [-3, -18, -2, -2, 1], 'lmfdb_label': '7056.bg4', 'torsion': [4]}
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id: 371414
{'degree': 4, 'field': [16, 10, -4, -1, 1], 'lmfdb_label': '7056.bg4', 'torsion': [2, 4]}
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id: 371415
{'degree': 6, 'field': [189, 0, 126, 0, 21, 0, 1], 'lmfdb_label': '7056.bg4', 'torsion': [14]}
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id: 371418
{'degree': 8, 'field': [-147, 0, -147, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '7056.bg4', 'torsion': [6]}
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id: 371416
{'degree': 8, 'field': [36, -72, 72, -24, 13, -10, 2, -2, 1], 'lmfdb_label': '7056.bg4', 'torsion': [4, 4]}
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id: 371417
{'degree': 8, 'field': [214, 24, 23, -82, 12, 32, -6, -4, 1], 'lmfdb_label': '7056.bg4', 'torsion': [2, 8]}
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id: 371419
{'degree': 12, 'field': [729, 0, 243, 0, 81, 0, 27, 0, 9, 0, 3, 0, 1], 'lmfdb_label': '7056.bg4', 'torsion': [2, 14]}
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id: 371421
{'degree': 16, 'field': [232, 488, -388, -924, 2530, -3200, 2268, -1090, 473, -350, 334, -222, 128, -70, 30, -8, 1], 'lmfdb_label': '7056.bg4', 'torsion': [4, 8]}
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id: 371420
{'degree': 16, 'field': [484, 2024, -6988, 13296, -15878, 13336, -8154, 2948, -163, -896, 826, -540, 272, -112, 36, -8, 1], 'lmfdb_label': '7056.bg4', 'torsion': [8]}
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id: 371423
{'degree': 16, 'field': [21609, 0, -21609, 0, 15435, 0, -6174, 0, 1911, 0, -294, 0, 42, 0, 0, 0, 1], 'lmfdb_label': '7056.bg4', 'torsion': [6, 6]}
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id: 371422
{'degree': 16, 'field': [208378, -34616, -169856, 21876, 98181, -20356, -30918, 8246, 6415, -1442, -983, 56, 131, 18, -15, -2, 1], 'lmfdb_label': '7056.bg4', 'torsion': [2, 16]}
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id: 371424
{'degree': 20, 'field': [10916801973, 0, 0, 0, 346565142, 0, 0, 0, 2750517, 0, -166698, 0, 31752, 0, 2646, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '7056.bg4', 'torsion': [2, 22]}
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ec_localdata • Show schema
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id: 144759
{'conductor': 7056, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '7056.bg4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 144760
{'conductor': 7056, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '7056.bg4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 144761
{'conductor': 7056, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '7056.bg4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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lmfdb_label 7056.bg4 does not appear in ec_galrep
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lmfdb_iso 7056.bg does not appear in ec_padic