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ec_curvedata • Show schema
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{'Ciso': '412224b', 'Clabel': '412224b2', 'Cnumber': 2, 'abc_quality': 1.0060248717974618, 'absD': 98289383681517165622591488, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 456, 'ainvs': [0, -1, 0, 99082015, 288785548161], 'analytic_rank': 0, 'bad_primes': [2, 3, 19, 113], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 412224, 'degree': 242810880, 'elladic_images': ['8.6.0.5'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.6748022256768453524838752215', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2], 'jinv': [410363075617640914325831, 374944243169850027552], 'lmfdb_iso': '412224.b', 'lmfdb_label': '412224.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 1548157, -563453715], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.a.1', '228.6.0.?', '456.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1], [3, 4, 137408], [13, 2, 137408], [19, 20, 21696], [113, 114, 3648]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '2.6350814548369273883580270393', 'prec': 100}, 'szpiro_ratio': 5.170261645785413, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, -1, 0, -4, 0, 4, 0, 1, 0, 0, 0, 0, 0, 4, 0, -6, 0, 1, 0], 'aplist': [0, -1, -4, 4, 0, 0, -6, 1, -6, 6, -10, 12, 10, -4, 6, -2, -12, -6, -8, 0, -10, -10, 12, 6, 6], 'class_deg': 2, 'class_size': 2, 'conductor': 412224, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '412224.b', 'trace_hash': 1145820694238199992}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00064284658717004650288911604388', 'prec': 113}, 'conductor': 412224, 'gens': [], 'heights': [], 'lmfdb_label': '412224.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.039147907850851019953655496107', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.31318326280680815962924396885273214386', 'prec': 133}, 'tamagawa_product': 32, 'torsion_generators': [[-2713, 0, 1]], 'xcoord_integral_points': [-2713]}
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lmfdb_label 412224.b2 does not appear in ec_iwasawa
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lmfdb_label 412224.b2 does not appear in ec_torsion_growth
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ec_localdata • Show schema
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id: 10187723
{'conductor': 412224, 'conductor_valuation': 6, 'discriminant_valuation': 23, 'j_denominator_valuation': 5, 'kodaira_symbol': -17, 'lmfdb_label': '412224.b2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 10187724
{'conductor': 412224, 'conductor_valuation': 1, 'discriminant_valuation': 26, 'j_denominator_valuation': 26, 'kodaira_symbol': 30, 'lmfdb_label': '412224.b2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 10187725
{'conductor': 412224, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '412224.b2', 'prime': 19, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 10187726
{'conductor': 412224, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '412224.b2', 'prime': 113, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 4214957
{'adelic_gens': [[1, 2, 2, 5], [305, 4, 154, 9], [1, 4, 0, 1], [97, 4, 194, 9], [172, 289, 57, 400], [453, 4, 452, 5], [2, 1, 227, 0], [1, 0, 4, 1], [3, 4, 8, 11]], 'adelic_image': '456.12.0.?', 'conductor': 412224, 'lmfdb_label': '412224.b2', 'prime': 0}
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id: 1394883
{'conductor': 412224, 'elladic_image': '8.6.0.5', 'lmfdb_label': '412224.b2', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 412224.b does not appear in ec_padic