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ec_curvedata • Show schema
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{'Ciso': '411840nt', 'Clabel': '411840nt5', 'Cnumber': 5, 'abc_quality': 0.9984292783090328, 'absD': 15344944902144000000000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 17160, 'ainvs': [0, 0, 0, 46321908, 144207134224], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 11, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 411840, 'degree': 84934656, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.5183794263656163789759156837', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 357, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [57519563401957999679, 80296734375000000], 'lmfdb_iso': '411840.nt', 'lmfdb_label': '411840.nt8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 80420, 10438352], 'min_quad_twist_disc': 24, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.48.0.c.3', '24.96.0-12.c.3.3', '78.24.0.?', '104.12.0.?', '156.96.1.?', '312.192.1.?', '440.12.0.?', '1320.192.1.?', '5720.24.0.?', '17160.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.6635520391047686434955639579', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.9293525111916435691524448831', 'prec': 100}, 'szpiro_ratio': 5.020901874600744, '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, 1, 0, -1, 0, 0, 0, 6, 0, -4, 0], 'aplist': [0, 0, 1, 4, 1, -1, 6, -4, 0, -6, 4, -2, 6, -4, 0, -6, -12, 10, -4, 0, 2, -8, -12, 6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 411840, 'isogeny_matrix': [[1, 2, 4, 4, 3, 6, 12, 12], [2, 1, 2, 2, 6, 3, 6, 6], [4, 2, 1, 4, 12, 6, 3, 12], [4, 2, 4, 1, 12, 6, 12, 3], [3, 6, 12, 12, 1, 2, 4, 4], [6, 3, 6, 6, 2, 1, 2, 2], [12, 6, 3, 12, 4, 2, 1, 4], [12, 6, 12, 3, 4, 2, 4, 1]], 'lmfdb_iso': '411840.nt', 'trace_hash': 453344588004329785}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00087897082431878164246155454755', 'prec': 113}, 'conductor': 411840, 'gens': [[24258, 3942400, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.6635520391047686434955639579', 'prec': 100}], 'lmfdb_label': '411840.nt8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.047279189804781931199781315997', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.089335911527836932379347921132260910', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[-2692, 0, 1]], 'xcoord_integral_points': [-2692, 24258]}
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lmfdb_label 411840.nt8 does not appear in ec_iwasawa
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lmfdb_label 411840.nt8 does not appear in ec_torsion_growth
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ec_localdata • Show schema
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id: 10180382
{'conductor': 411840, 'conductor_valuation': 6, 'discriminant_valuation': 24, 'j_denominator_valuation': 6, 'kodaira_symbol': -18, 'lmfdb_label': '411840.nt8', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 10180383
{'conductor': 411840, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '411840.nt8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 10180384
{'conductor': 411840, 'conductor_valuation': 1, 'discriminant_valuation': 12, 'j_denominator_valuation': 12, 'kodaira_symbol': 16, 'lmfdb_label': '411840.nt8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 12}
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id: 10180385
{'conductor': 411840, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '411840.nt8', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 10180386
{'conductor': 411840, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '411840.nt8', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 4213124
{'adelic_gens': [[7936, 3, 6141, 17074], [10297, 24, 3444, 289], [1, 12, 12, 145], [17144, 8577, 3319, 5806], [7801, 24, 7812, 289], [17137, 24, 17136, 25], [15, 106, 15854, 7931], [1, 24, 0, 1], [9279, 12152, 14044, 16531], [1, 0, 24, 1], [4289, 17136, 4290, 17159]], 'adelic_image': '17160.384.5.?', 'conductor': 411840, 'lmfdb_label': '411840.nt8', 'prime': 0}
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id: 1393969
{'conductor': 411840, 'elladic_image': '4.6.0.1', 'lmfdb_label': '411840.nt8', 'modell_image': '2B', 'prime': 2}
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id: 1393970
{'conductor': 411840, 'elladic_image': '3.4.0.1', 'lmfdb_label': '411840.nt8', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 411840.nt does not appear in ec_padic