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ec_curvedata • Show schema
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{'Ciso': '32448ci', 'Clabel': '32448ci6', 'Cnumber': 6, 'abc_quality': 1.2105879594055395, 'absD': 5693935583232, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 624, 'ainvs': [0, -1, 0, -259809, 51058305], 'analytic_rank': 0, 'bad_primes': [2, 3, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 32448, 'degree': 147456, 'elladic_images': ['16.48.0.210'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6768431634908290594935812261', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 13, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [3065617154, 9], 'lmfdb_iso': '32448.n', 'lmfdb_label': '32448.n1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -384, -2772], 'min_quad_twist_disc': -104, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.r.1', '16.48.0.l.1', '24.48.0.bf.1', '48.96.1.bv.1', '52.12.0-4.c.1.2', '104.48.0.?', '208.96.0.?', '312.96.0.?', '624.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, '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': '-0.58759002103319516354090800008', 'prec': 107}, 'szpiro_ratio': 4.718865246215369, '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, -4, 0, 0, 0, 2, 0, 2, 0, 4, 0], 'aplist': [0, -1, -2, 0, -4, 0, 2, 4, 8, -6, 8, 6, 6, 4, 0, 2, -4, 2, 4, 8, -10, 8, 4, 6, -2], 'class_deg': 8, 'class_size': 6, 'conductor': 32448, 'isogeny_matrix': [[1, 8, 2, 4, 8, 4], [8, 1, 4, 2, 4, 8], [2, 4, 1, 2, 4, 2], [4, 2, 2, 1, 2, 4], [8, 4, 4, 2, 1, 8], [4, 8, 2, 4, 8, 1]], 'lmfdb_iso': '32448.n', 'trace_hash': 1374267989891345265}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.034955259787802296928485512829', 'prec': 107}, 'conductor': 32448, 'gens': [], 'heights': [], 'lmfdb_label': '32448.n1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.66120568878733753217957347891', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3224113775746750643591469578225552966', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[295, 0, 1]], 'xcoord_integral_points': [295]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [0, 0], '13': 'a'}, 'iwp0': 3, 'lmfdb_label': '32448.n1'}
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ec_torsion_growth • Show schema
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id: 1615579
{'degree': 2, 'field': [-26, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [4]}
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id: 1615580
{'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '32448.n1', 'torsion': [4]}
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id: 1615578
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [2, 2]}
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id: 1615581
{'degree': 4, 'field': [-1, 10, -9, -2, 1], 'lmfdb_label': '32448.n1', 'torsion': [2, 4]}
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id: 1615583
{'degree': 4, 'field': [25, 0, -16, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [8]}
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id: 1615582
{'degree': 4, 'field': [169, 0, -52, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [8]}
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id: 1615588
{'degree': 8, 'field': [-85683, 0, 21970, 0, -1014, 0, 0, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [6]}
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id: 1615587
{'degree': 8, 'field': [-407, 1372, -436, -644, 220, 92, -28, -4, 1], 'lmfdb_label': '32448.n1', 'torsion': [16]}
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id: 1615586
{'degree': 8, 'field': [-23, 76, 16, -164, 33, 56, -14, -4, 1], 'lmfdb_label': '32448.n1', 'torsion': [2, 8]}
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id: 1615585
{'degree': 8, 'field': [147, 28, 30, -104, 23, 32, -6, -4, 1], 'lmfdb_label': '32448.n1', 'torsion': [8]}
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id: 1615584
{'degree': 8, 'field': [1897, 3624, 2760, 336, 206, -24, 24, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [2, 4]}
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id: 1615592
{'degree': 16, 'field': [433, 3132, -11028, -13500, 42976, 9648, -51336, 324, 26289, -1344, -6588, 252, 826, -12, -48, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [2, 16]}
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id: 1615590
{'degree': 16, 'field': [2393, 6448, 9088, 12832, 11472, 12336, 15800, 3296, 10849, -96, 3364, -104, 502, -8, 36, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [2, 8]}
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id: 1615595
{'degree': 16, 'field': [3351, 3624, 17714, -16432, -48778, 45856, 17752, -20000, -3831, 3636, 1200, -656, -194, 112, 4, -8, 1], 'lmfdb_label': '32448.n1', 'torsion': [12]}
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id: 1615589
{'degree': 16, 'field': [29241, 12312, 50760, -137592, 112824, -89352, 71664, -672, -37847, 16360, 5044, -3704, -50, 280, -20, -8, 1], 'lmfdb_label': '32448.n1', 'torsion': [4, 4]}
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id: 1615591
{'degree': 16, 'field': [339433, 668664, 700584, 450192, 767080, 858648, 285672, -197280, 120438, 1224, -26760, 720, 2056, -24, -72, 0, 1], 'lmfdb_label': '32448.n1', 'torsion': [16]}
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id: 1615593
{'degree': 16, 'field': [1514239, 8240968, 3822654, 2427340, -2683136, -1410792, -196176, 98964, -57216, 7776, -2514, -240, 178, 16, 12, -8, 1], 'lmfdb_label': '32448.n1', 'torsion': [2, 6]}
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id: 1615594
{'degree': 16, 'field': [2757995423, -2744220904, 727274886, 271170016, -183991406, 19137192, 7654340, -549148, -761520, 134984, 23606, -10404, 624, 48, 24, -8, 1], 'lmfdb_label': '32448.n1', 'torsion': [12]}
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ec_localdata • Show schema
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id: 758976
{'conductor': 32448, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '32448.n1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 758977
{'conductor': 32448, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '32448.n1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 758978
{'conductor': 32448, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '32448.n1', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1880926
{'adelic_gens': [[1, 16, 0, 1], [428, 299, 585, 350], [479, 0, 0, 623], [365, 208, 208, 261], [5, 4, 620, 621], [77, 416, 234, 155], [1, 0, 16, 1], [15, 2, 526, 611], [609, 16, 608, 17]], 'adelic_image': '624.192.1.?', 'conductor': 32448, 'lmfdb_label': '32448.n1', 'prime': 0}
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id: 145089
{'conductor': 32448, 'elladic_image': '16.48.0.210', 'lmfdb_label': '32448.n1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 32448.n does not appear in ec_padic