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ec_curvedata • Show schema
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{'Ciso': '187425by', 'Clabel': '187425by1', 'Cnumber': 1, 'abc_quality': 0.6890595357104303, 'absD': 1447055126015625, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 7140, 'ainvs': [1, -1, 1, -36980, -2025978], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 187425, 'degree': 688128, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6181948107215793872236053323', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 28, 'isogeny_degrees': [1, 2], 'jinv': [328509, 85], 'lmfdb_iso': '187425.bc', 'lmfdb_label': '187425.bc1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -272, -1214], 'min_quad_twist_disc': 105, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '84.6.0.?', '340.6.0.?', '3570.6.0.?', '7140.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.8056913707593175502339640824', 'prec': 100}, 'semistable': False, 'serre_invariants': [[3, 6, 20825], [5, 18, 7497], [7, 20, 3825], [17, 18, 11025]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.92060982945398320175460020113', 'prec': 107}, 'szpiro_ratio': 3.5555142574108705, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, -1, 0, 0, 0, 3, 0, 0, -4, 0, 2, 0, 0, -1, 1, 0, 8, 0], 'aplist': [-1, 0, 0, 0, -4, 2, 1, 8, 0, -2, 0, -6, -6, 6, -2, -6, -4, -6, -2, 0, -4, -2, 2, 14, 12], 'class_deg': 2, 'class_size': 2, 'conductor': 187425, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '187425.bc', 'trace_hash': 2090703372696415193}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.039305547140934696437701259528', 'prec': 107}, 'conductor': 187425, 'gens': [[228, 1050, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '5.8056913707593175502339640824', 'prec': 100}], 'lmfdb_label': '187425.bc1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.35086956245554864001866801842', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0740807820205523291740552118244094271', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-61, 30, 1]], 'xcoord_integral_points': [-61, 228]}
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lmfdb_label 187425.bc1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 8263719
{'degree': 2, 'field': [-446, -1, 1], 'lmfdb_label': '187425.bc1', 'torsion': [2, 2]}
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id: 8263720
{'degree': 4, 'field': [256, -32, 54, -2, 1], 'lmfdb_label': '187425.bc1', 'torsion': [4]}
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id: 8263723
{'degree': 8, 'field': [-235791, 130788, 61380, 13671, 1125, -231, -12, 0, 1], 'lmfdb_label': '187425.bc1', 'torsion': [6]}
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id: 8263721
{'degree': 8, 'field': [256, -2720, 9998, -14726, 7789, -514, 176, -4, 1], 'lmfdb_label': '187425.bc1', 'torsion': [2, 4]}
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id: 8263722
{'degree': 8, 'field': [126736, 0, -414677, 0, 10359, 0, 157, 0, 1], 'lmfdb_label': '187425.bc1', 'torsion': [2, 4]}
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id: 8263724
{'degree': 16, 'field': [14478105625, 0, 1230797500, 0, 50978150, 0, 7021900, 0, 562195, 0, 5900, 0, 794, 0, -16, 0, 1], 'lmfdb_label': '187425.bc1', 'torsion': [8]}
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id: 8263725
{'degree': 16, 'field': [53187890625, 0, -51041292750, 0, 1747858725, 0, -16460325, 0, 4333500, 0, -129255, 0, 3480, 0, 0, 0, 1], 'lmfdb_label': '187425.bc1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 4638471
{'conductor': 187425, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '187425.bc1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 4638472
{'conductor': 187425, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '187425.bc1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 4638473
{'conductor': 187425, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '187425.bc1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 4638474
{'conductor': 187425, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '187425.bc1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2868067
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [7137, 4, 7136, 5], [1, 4, 0, 1], [3064, 1, 1019, 0], [2384, 1, 4759, 0], [2522, 1, 5879, 0], [5714, 1, 4283, 0], [1789, 5356, 1784, 5355]], 'adelic_image': '7140.12.0.?', 'conductor': 187425, 'lmfdb_label': '187425.bc1', 'prime': 0}
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id: 700240
{'conductor': 187425, 'elladic_image': '2.3.0.1', 'lmfdb_label': '187425.bc1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 187425.bc does not appear in ec_padic