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ec_curvedata • Show schema
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{'Ciso': '439824r', 'Clabel': '439824r1', 'Cnumber': 1, 'abc_quality': 0.933285229740939, 'absD': 142739763167232, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 952, 'ainvs': [0, -1, 0, -303424, 64430080], 'analytic_rank': 1, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 439824, 'degree': 2654208, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7912144310602005176056165308', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2, 4], 'jinv': [6411014266033, 296208], 'lmfdb_iso': '439824.r', 'lmfdb_label': '439824.r3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -387, 2769], 'min_quad_twist_disc': 28, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '28.12.0-4.c.1.1', '34.6.0.a.1', '56.24.0-8.m.1.4', '68.12.0.g.1', '136.24.0.?', '476.24.0.?', '952.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0228952617389294265976216867', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.12511217597259855563570803762', 'prec': 103}, 'szpiro_ratio': 3.8080476299301442, '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, -2, 0, 0, 0, 1, 0, -1, 0, 2, 0, 2, 0, -1, 0, 4, 0], 'aplist': [0, -1, -2, 0, -1, 2, -1, 4, 4, -6, -4, 2, -10, -4, -8, 6, -4, 6, -12, 12, -2, -4, -4, -10, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 439824, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '439824.r', 'trace_hash': 877382397208400949}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.027808074185690560139855069921', 'prec': 107}, 'conductor': 439824, 'gens': [[352, 1056, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0228952617389294265976216867', 'prec': 100}], 'lmfdb_label': '439824.r3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.54681793141770564063040850838', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.4746997686484317744767741237622430195', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[320, 0, 1]], 'xcoord_integral_points': [320, 321, 352, 418, 3456]}
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lmfdb_label 439824.r3 does not appear in ec_iwasawa
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lmfdb_label 439824.r3 does not appear in ec_torsion_growth
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ec_localdata • Show schema
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id: 10859571
{'conductor': 439824, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '439824.r3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 10859572
{'conductor': 439824, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '439824.r3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 10859573
{'conductor': 439824, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '439824.r3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 10859574
{'conductor': 439824, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '439824.r3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 10859575
{'conductor': 439824, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '439824.r3', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 4375858
{'adelic_gens': [[1, 8, 0, 1], [568, 819, 525, 274], [1, 0, 8, 1], [603, 462, 770, 155], [945, 8, 944, 9], [111, 252, 658, 321], [1, 4, 4, 17], [543, 0, 0, 951], [7, 6, 946, 947]], 'adelic_image': '952.48.0.?', 'conductor': 439824, 'lmfdb_label': '439824.r3', 'prime': 0}
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id: 1476022
{'conductor': 439824, 'elladic_image': '8.12.0.11', 'lmfdb_label': '439824.r3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 439824.r does not appear in ec_padic