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ec_curvedata • Show schema
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{'Ciso': '398544i', 'Clabel': '398544i1', 'Cnumber': 1, 'abc_quality': 0.9587220688319041, 'absD': 52294328517169152, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 20976, 'ainvs': [0, -1, 0, -32657624, 71844049200], 'analytic_rank': 1, 'bad_primes': [2, 3, 19, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 398544, 'degree': 17971200, 'elladic_images': ['16.24.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.7643671299556919886546183588', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 8, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [19989223566735457, 271377], 'lmfdb_iso': '398544.i', 'lmfdb_label': '398544.i4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5654, 161282], 'min_quad_twist_disc': 76, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.n.1', '12.12.0-4.c.1.1', '16.24.0-8.n.1.2', '24.24.0-8.n.1.5', '48.48.0-48.f.2.10', '76.12.0.?', '114.6.0.?', '152.24.0.?', '184.24.0.?', '228.24.0.?', '304.48.0.?', '368.48.0.?', '456.48.0.?', '552.48.0.?', '912.96.0.?', '1104.96.0.?', '3496.48.0.?', '6992.96.0.?', '10488.96.0.?', '20976.192.1.?'], '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': '6.6469180374293975477203899202', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 1083], [3, 4, 132848], [19, 200, 1104], [23, 24, 17328]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.59900045981252644923287252140', 'prec': 103}, 'szpiro_ratio': 4.925594917824191, '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, 2, 0, 2, 0, -6, 0, 0, 0], 'aplist': [0, -1, -2, 0, 4, 2, -6, 0, -1, 2, 8, 2, 6, 12, 0, -6, 4, 14, 12, 0, 10, 8, 12, 6, -10], 'class_deg': 8, 'class_size': 6, 'conductor': 398544, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '398544.i', 'trace_hash': 202503810032413308}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0039710121787645027783027556347', 'prec': 110}, 'conductor': 398544, 'gens': [[-3662, 377246, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '6.6469180374293975477203899202', 'prec': 100}], 'lmfdb_label': '398544.i4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.25151147406283373406324497476', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.6871046142748225138526623258533196405', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[3300, 0, 1]], 'xcoord_integral_points': [-3662, 3300]}
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lmfdb_label 398544.i4 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 16441379
{'degree': 2, 'field': [-19, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [4]}
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id: 16441378
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '398544.i4', 'torsion': [2, 2]}
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id: 16441380
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [4]}
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id: 16441382
{'degree': 4, 'field': [-15, 72, -71, -2, 1], 'lmfdb_label': '398544.i4', 'torsion': [8]}
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id: 16441383
{'degree': 4, 'field': [1, 0, -21, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [8]}
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id: 16441381
{'degree': 4, 'field': [16, 0, -11, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [2, 4]}
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id: 16441387
{'degree': 8, 'field': [-9747, 0, -9443, 0, 342, 0, 0, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [6]}
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id: 16441385
{'degree': 8, 'field': [253, -142, 172, -58, 25, 2, 4, -4, 1], 'lmfdb_label': '398544.i4', 'torsion': [8]}
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id: 16441386
{'degree': 8, 'field': [2809, 0, -2382, 0, 623, 0, -54, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [2, 8]}
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id: 16441384
{'degree': 8, 'field': [909203409, 0, 0, 0, 30153, 0, 0, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [2, 4]}
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id: 16441392
{'degree': 16, 'field': [361, 0, 172615, 0, 1147, 0, -129007, 0, 4226, 0, -8257, 0, 565, 0, 46, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [2, 6]}
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id: 16441389
{'degree': 16, 'field': [38416, 5488, 392, 24360, -5512, -4156, 7186, -2814, 313, 642, -440, 154, -13, -12, 8, -4, 1], 'lmfdb_label': '398544.i4', 'torsion': [2, 8]}
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id: 16441394
{'degree': 16, 'field': [123201, 0, -15928032, 0, 7642792, 0, -868773, 0, 68688, 0, 4781, 0, -255, 0, -6, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [12]}
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id: 16441393
{'degree': 16, 'field': [68939809, 0, -29027288, 0, 3055504, 0, -4053669, 0, 476520, 0, -3363, 0, 361, 0, -38, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [12]}
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id: 16441390
{'degree': 16, 'field': [930067009, 0, -1449068873, 0, 806459983, 0, -189773063, 0, 17835154, 0, -804833, 0, 18757, 0, -218, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [2, 16]}
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id: 16441391
{'degree': 16, 'field': [9618705625, 0, 18314495575, 0, 30451407991, 0, 807966301, 0, 12677712, 0, -1307299, 0, 20167, 0, -169, 0, 1], 'lmfdb_label': '398544.i4', 'torsion': [16]}
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id: 16441388
{'degree': 16, 'field': [17868678762496, -5840346365952, 954453491712, -103987150848, 19324651456, -2088680832, -46964736, 2643792, 7905441, -726474, -27342, -3852, 2839, -36, 18, -6, 1], 'lmfdb_label': '398544.i4', 'torsion': [4, 4]}
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ec_localdata • Show schema
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id: 9858752
{'conductor': 398544, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '398544.i4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 9858753
{'conductor': 398544, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '398544.i4', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 9858754
{'conductor': 398544, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '398544.i4', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 9858755
{'conductor': 398544, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '398544.i4', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 4136201
{'adelic_gens': [[12128, 20971, 14397, 14], [1, 16, 0, 1], [15, 2, 20878, 20963], [20961, 16, 20960, 17], [1, 0, 16, 1], [5, 4, 20972, 20973], [1, 16, 15740, 15861], [7855, 20960, 2686, 15825], [4573, 16, 11600, 20661], [7000, 1, 14063, 10]], 'adelic_image': '20976.192.1.?', 'conductor': 398544, 'lmfdb_label': '398544.i4', 'prime': 0}
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id: 1355722
{'conductor': 398544, 'elladic_image': '16.24.0.8', 'lmfdb_label': '398544.i4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 398544.i does not appear in ec_padic