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ec_curvedata • Show schema
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{'Ciso': '1728t', 'Clabel': '1728t1', 'Cnumber': 1, 'abc_quality': 0.9463948908766787, 'absD': 3981312, 'adelic_genus': 0, 'adelic_index': 8, 'adelic_level': 12, 'ainvs': [0, 0, 0, -48, -160], 'analytic_rank': 0, 'bad_primes': [2, 3], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 1728, 'degree': 384, 'elladic_images': ['4.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.021021938319409758472850076029', 'prec': 110}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 27, 'isogeny_degrees': [1], 'jinv': [-3072, 1], 'lmfdb_iso': '1728.bb', 'lmfdb_label': '1728.bb1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -12, 20], 'min_quad_twist_disc': -8, 'modell_images': [], 'modm_images': ['4.4.0.a.1', '6.2.0.a.1', '12.8.0.c.1'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 27], [3, 8, 32]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2874487692510583242076397331', 'prec': 103}, 'szpiro_ratio': 3.1756381633216777, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 4, 0, 3, 0, 0, 0, -4, 0, -1, 0, 0, 0, 4, 0, -1, 0], 'aplist': [0, 0, 4, 3, -4, -1, 4, -1, 4, 0, 4, 9, 0, -8, -12, -8, -4, 5, 11, 8, 1, 5, -8, -12, 5], 'class_deg': 1, 'class_size': 1, 'conductor': 1728, 'isogeny_matrix': [[1]], 'lmfdb_iso': '1728.bb', 'trace_hash': 1516555706223705924}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.0429402384590180085931622166', 'prec': 100}, 'conductor': 1728, 'gens': [], 'heights': [], 'lmfdb_label': '1728.bb1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.89212528653259632918191485221', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6763758595977889875457445566351524372', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0, 0], '31': [0, 0], '37': [0, 0], '41': [0, 0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '1728.bb1'}
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ec_torsion_growth • Show schema
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id: 87936
{'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '1728.bb1', 'torsion': [2]}
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id: 87937
{'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '1728.bb1', 'torsion': [2, 2]}
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id: 87938
{'degree': 8, 'field': [-3, 0, 6, 0, 18, 0, 4, 0, 1], 'lmfdb_label': '1728.bb1', 'torsion': [3]}
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id: 87939
{'degree': 12, 'field': [-3, 0, 0, 0, 3, 0, 0, 0, -9, 0, 0, 0, 1], 'lmfdb_label': '1728.bb1', 'torsion': [4]}
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ec_localdata • Show schema
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id: 27715
{'conductor': 1728, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '1728.bb1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 27716
{'conductor': 1728, 'conductor_valuation': 3, 'discriminant_valuation': 5, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '1728.bb1', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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id: 1675350
{'adelic_gens': [[9, 4, 8, 5], [4, 9, 5, 1], [2, 1, 5, 3], [8, 3, 1, 4], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '12.8.0.?', 'conductor': 1728, 'lmfdb_label': '1728.bb1', 'prime': 0}
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id: 8489
{'conductor': 1728, 'elladic_image': '4.4.0.1', 'lmfdb_label': '1728.bb1', 'modell_image': '2G', 'prime': 2}
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lmfdb_iso 1728.bb does not appear in ec_padic
