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ec_curvedata • Show schema
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{'Ciso': '271440cd', 'Clabel': '271440cd3', 'Cnumber': 3, 'abc_quality': 0.9390084776053046, 'absD': 34779346617600000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9048, 'ainvs': [0, 0, 0, 484917, 252220282], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13, 29], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 271440, 'degree': 9437184, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4331936867787303814420334546', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 55, 'isogeny_degrees': [1, 2, 4], 'jinv': [4223169036960119, 11647532812500], 'lmfdb_iso': '271440.cd', 'lmfdb_label': '271440.cd4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, 3368, 147364], 'min_quad_twist_disc': 12, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '12.12.0-4.c.1.1', '104.12.0.?', '116.12.0.?', '312.24.0.?', '348.24.0.?', '3016.24.0.?', '9048.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1907403618847302263271787147', 'prec': 100}, 'szpiro_ratio': 4.1733435128507415, '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, -1, 0, 4, 0, 0, 0, -4, 0, 1, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 0, -1, 4, -4, 1, 6, 4, -8, -1, -8, -6, 2, 4, 0, 10, -8, -10, 8, -4, 14, 16, -16, -14, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 271440, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '271440.cd', 'trace_hash': 1300937160916920922}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0077011364234034622120387182663', 'prec': 110}, 'conductor': 271440, 'gens': [], 'heights': [], 'lmfdb_label': '271440.cd4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.14502831288324148324618865340', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3204530061318637319390184543367551342', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-394, 0, 1]], 'xcoord_integral_points': [-394]}
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lmfdb_label 271440.cd4 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 11595191
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [4]}
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id: 11595192
{'degree': 2, 'field': [22, -1, 1], 'lmfdb_label': '271440.cd4', 'torsion': [4]}
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id: 11595190
{'degree': 2, 'field': [29, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [2, 2]}
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id: 11595193
{'degree': 4, 'field': [64, 0, 13, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [2, 4]}
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id: 11595197
{'degree': 8, 'field': [-62208, 0, -126576, 0, -864, 0, 0, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [6]}
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id: 11595195
{'degree': 8, 'field': [841, 0, -116, 0, -405, 0, 4, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [8]}
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id: 11595194
{'degree': 8, 'field': [2401, 686, -588, 420, 235, -60, -12, -2, 1], 'lmfdb_label': '271440.cd4', 'torsion': [2, 4]}
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id: 11595196
{'degree': 8, 'field': [11988856, -147608, 178426, -62024, 31983, -1168, 394, -4, 1], 'lmfdb_label': '271440.cd4', 'torsion': [8]}
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id: 11595202
{'degree': 16, 'field': [2304, 0, 112512, 0, 359524, 0, 56256, 0, -8736, 0, -30472, 0, -336, 0, 0, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [12]}
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id: 11595198
{'degree': 16, 'field': [2401, 686, 98, 3360, -647, -1202, 2034, -826, 12, 320, -216, 70, 1, -12, 8, -4, 1], 'lmfdb_label': '271440.cd4', 'torsion': [4, 4]}
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id: 11595200
{'degree': 16, 'field': [95824521, 0, 255840, 0, -314339, 0, 90216, 0, 29232, 0, -6952, 0, 333, 0, 48, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [2, 8]}
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id: 11595199
{'degree': 16, 'field': [97003594116, 0, -107103367800, 0, 66280651992, 0, -7773928884, 0, 369616789, 0, -8220692, 0, 91254, 0, -488, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [2, 8]}
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id: 11595201
{'degree': 16, 'field': [1525998207969, 0, 129997644803, 0, 7584300313, 0, -21228870, 0, -5800522, 0, 108634, 0, 633, 0, -61, 0, 1], 'lmfdb_label': '271440.cd4', 'torsion': [2, 6]}
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id: 11595203
{'degree': 16, 'field': [6269114932288, 42976313536, -48875853936, 8890631552, 2928078656, -9134848704, 3524167504, -413313488, 106607025, -2318744, 599260, -77160, 15590, -1288, 204, -8, 1], 'lmfdb_label': '271440.cd4', 'torsion': [12]}
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ec_localdata • Show schema
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id: 6727177
{'conductor': 271440, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '271440.cd4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 6727178
{'conductor': 271440, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '271440.cd4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 6727179
{'conductor': 271440, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '271440.cd4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 6727180
{'conductor': 271440, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '271440.cd4', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 6727181
{'conductor': 271440, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '271440.cd4', 'prime': 29, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 3379996
{'adelic_gens': [[7, 6, 9042, 9043], [1393, 3024, 2556, 3049], [5659, 5658, 4914, 3403], [1, 0, 8, 1], [6031, 0, 0, 9047], [3392, 4893, 6405, 344], [6976, 3, 213, 6034], [1, 8, 0, 1], [1, 4, 4, 17], [9041, 8, 9040, 9]], 'adelic_image': '9048.48.0.?', 'conductor': 271440, 'lmfdb_label': '271440.cd4', 'prime': 0}
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id: 969903
{'conductor': 271440, 'elladic_image': '4.6.0.1', 'lmfdb_label': '271440.cd4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 271440.cd does not appear in ec_padic