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ec_curvedata • Show schema
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{'Ciso': '166635o', 'Clabel': '166635o1', 'Cnumber': 1, 'abc_quality': 0.8996512608144922, 'absD': 89393470797330945, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 19320, 'ainvs': [1, -1, 1, -111983, 1082342], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 166635, 'degree': 1486848, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9422401695156765137267493172', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2, 4], 'jinv': [1439069689, 828345], 'lmfdb_iso': '166635.m', 'lmfdb_label': '166635.m4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -24, 1], 'min_quad_twist_disc': 69, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '60.12.0-4.c.1.2', '92.12.0.?', '168.12.0.?', '280.12.0.?', '690.6.0.?', '840.24.0.?', '1380.24.0.?', '3864.24.0.?', '6440.24.0.?', '19320.48.0.?'], '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': '1.5158742735739989207580914084', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.17481308278295317737424971717', 'prec': 107}, 'szpiro_ratio': 3.866733112321436, '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, -1, 0, -1, 3, 0, 1, -4, 0, 2, 1, 0, -1, 6, 0, 4, 1], 'aplist': [-1, 0, -1, -1, -4, 2, 6, 4, 0, -6, 8, -6, -6, -4, 0, -10, 0, -10, 12, 8, 14, -4, 0, 6, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 166635, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '166635.m', 'trace_hash': 68191188028274784}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.020558509440954024789788662384', 'prec': 107}, 'conductor': 166635, 'gens': [[765, 18661, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.5158742735739989207580914084', 'prec': 100}], 'lmfdb_label': '166635.m4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.28954762555135776454055680358', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.5113423723819256004829524180815128553', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-339, 169, 1]], 'xcoord_integral_points': [-339, 765]}
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lmfdb_label 166635.m4 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 7429795
{'degree': 2, 'field': [-86, -1, 1], 'lmfdb_label': '166635.m4', 'torsion': [2, 2]}
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id: 7429797
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '166635.m4', 'torsion': [4]}
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id: 7429796
{'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '166635.m4', 'torsion': [4]}
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id: 7429798
{'degree': 4, 'field': [4, 0, 19, 0, 1], 'lmfdb_label': '166635.m4', 'torsion': [2, 4]}
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id: 7429802
{'degree': 8, 'field': [-951479, 319664, -322898, 6467, -3230, -7, 7, -4, 1], 'lmfdb_label': '166635.m4', 'torsion': [6]}
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id: 7429800
{'degree': 8, 'field': [417, -474, 1509, -714, 460, -98, 9, -2, 1], 'lmfdb_label': '166635.m4', 'torsion': [8]}
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id: 7429801
{'degree': 8, 'field': [9781, -23761, 42804, -34777, 10274, -179, -44, -3, 1], 'lmfdb_label': '166635.m4', 'torsion': [8]}
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id: 7429799
{'degree': 8, 'field': [34516, 110936, 63104, -18448, 2389, 574, -94, -2, 1], 'lmfdb_label': '166635.m4', 'torsion': [2, 4]}
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id: 7429804
{'degree': 16, 'field': [565524, -5193216, 23646312, -4434048, 10932333, 3950256, 728436, 954936, 45496, 26324, 11998, -472, 1108, 8, 52, -4, 1], 'lmfdb_label': '166635.m4', 'torsion': [2, 8]}
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id: 7429808
{'degree': 16, 'field': [1124844901, -2302915024, 1359895830, -543406085, 451567340, -46760127, 6705103, -275590, 334530, -228670, 24868, -897, 980, -35, 15, -4, 1], 'lmfdb_label': '166635.m4', 'torsion': [12]}
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id: 7429807
{'degree': 16, 'field': [1570933225, 0, 759284488, 0, 83810080, 0, -6080699, 0, -919388, 0, 25135, 0, 865, 0, 46, 0, 1], 'lmfdb_label': '166635.m4', 'torsion': [12]}
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id: 7429803
{'degree': 16, 'field': [14331920656, 0, 0, 0, 88762984, 0, 0, 0, 376401, 0, 0, 0, 694, 0, 0, 0, 1], 'lmfdb_label': '166635.m4', 'torsion': [4, 4]}
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id: 7429806
{'degree': 16, 'field': [54109273921, 176011578521, -60524036580, -13006835405, -2084264515, 2967217788, -333371507, 55703915, -13400910, -2603455, 476263, -3552, 3770, 595, -165, -4, 1], 'lmfdb_label': '166635.m4', 'torsion': [2, 6]}
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id: 7429805
{'degree': 16, 'field': [89697894400, -11974297600, 5146041600, -7733512000, -237612560, -49317000, 230124320, 45842410, 3811881, -1114211, -336325, -13524, 7864, 326, -105, -1, 1], 'lmfdb_label': '166635.m4', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 4125396
{'conductor': 166635, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '166635.m4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 4125397
{'conductor': 166635, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '166635.m4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 4125398
{'conductor': 166635, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '166635.m4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 4125399
{'conductor': 166635, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '166635.m4', 'prime': 23, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 2740846
{'adelic_gens': [[19313, 8, 19312, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [6436, 19319, 12857, 19314], [16913, 16908, 16910, 7247], [4192, 19317, 5035, 19318], [7, 6, 19314, 19315], [2419, 2418, 7258, 16915], [2761, 8, 11044, 33], [7736, 3, 5, 2]], 'adelic_image': '19320.48.0.?', 'conductor': 166635, 'lmfdb_label': '166635.m4', 'prime': 0}
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id: 631756
{'conductor': 166635, 'elladic_image': '4.6.0.1', 'lmfdb_label': '166635.m4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 166635.m does not appear in ec_padic