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ec_curvedata • Show schema
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{'Ciso': '7728r', 'Clabel': '7728r5', 'Cnumber': 5, 'abc_quality': 1.0156853826442096, 'absD': 2611642496827392, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2576, 'ainvs': [0, 1, 0, -1266144, 547941492], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 23], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 7728, 'degree': 98304, 'elladic_images': ['16.48.0.32'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.1091217335997830208422237035', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [54804145548726848737, 637608031452], 'lmfdb_iso': '7728.o', 'lmfdb_label': '7728.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -79134, -8601153], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.2', '16.48.0-16.e.2.7', '28.24.0-28.h.1.2', '56.48.0-56.bj.1.9', '112.96.0.?', '184.48.0.?', '368.96.0.?', '1288.96.0.?', '2576.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.4159745530398377114249915820', 'prec': 100}, 'szpiro_ratio': 6.005856554918792, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, -2, 0, -1, 0, 1, 0, 4, 0, -2, 0, -2, 0, -6, 0, -4, 0], 'aplist': [0, 1, -2, -1, 4, -2, -6, -4, 1, -2, 8, 6, -6, 4, 8, 6, -4, -10, -4, 8, -6, 0, 12, 2, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 7728, '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': '7728.o', 'trace_hash': 914201361978304918}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.014724485845033076786463497595', 'prec': 107}, 'conductor': 7728, 'gens': [], 'heights': [], 'lmfdb_label': '7728.o1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.41382914741244632531290295725', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.6553165896497853012516118289840482818', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[732, 3726, 1]], 'xcoord_integral_points': [651, 732]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '7': [0, 0], '23': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '7728.o1'}
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ec_torsion_growth • Show schema
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id: 404427
{'degree': 2, 'field': [-322, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [8]}
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id: 404426
{'degree': 2, 'field': [-46, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [8]}
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id: 404425
{'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [2, 4]}
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id: 404428
{'degree': 4, 'field': [1521, 0, -106, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [2, 8]}
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id: 404433
{'degree': 8, 'field': [-768, 0, -316, 0, -96, 0, 0, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [12]}
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id: 404430
{'degree': 8, 'field': [36, 0, 88, 0, -8, 0, 4, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [2, 8]}
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id: 404429
{'degree': 8, 'field': [63001, -20582, 3362, -584, 503, -80, 2, -2, 1], 'lmfdb_label': '7728.o1', 'torsion': [4, 4]}
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id: 404431
{'degree': 8, 'field': [103684, 0, -59248, 0, 6164, 0, -184, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [16]}
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id: 404432
{'degree': 8, 'field': [157703364, 0, 3317888, 0, 13524, 0, 0, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [16]}
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id: 404436
{'degree': 16, 'field': [-120439471, -253401304, 208933144, 664950608, 211019736, -198221544, -84620392, 22871200, 10763902, -1150920, -613976, 24656, 16888, -184, -216, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [2, 16]}
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id: 404434
{'degree': 16, 'field': [6561, 0, 0, 0, 796030, 0, 0, 0, 4371, 0, 0, 0, 414, 0, 0, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [4, 8]}
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id: 404438
{'degree': 16, 'field': [4343056, 0, -4527968, 0, 1255312, 0, 136993, 0, -45422, 0, -2711, 0, 25, 0, -14, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [2, 12]}
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id: 404435
{'degree': 16, 'field': [212838921, 0, 39186792, 0, -4253396, 0, -616168, 0, 87486, 0, 952, 0, -420, 0, 8, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [2, 16]}
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id: 404439
{'degree': 16, 'field': [1836036801, 0, -319310748, 0, 13883076, 0, -186252436, 0, 7840838, 0, -104788, 0, 2116, 0, -92, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [24]}
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id: 404437
{'degree': 16, 'field': [44791229390625, 0, -5206592584800, 0, 253930770576, 0, -6542602864, 0, 91902818, 0, -890848, 0, 15568, 0, 16, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [2, 16]}
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id: 404440
{'degree': 16, 'field': [48134316968878336, 0, -4783534605602816, 0, 138222577045504, 0, -1909006582784, 0, 14820176224, 0, -71316560, 0, 242305, 0, -644, 0, 1], 'lmfdb_label': '7728.o1', 'torsion': [24]}
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ec_localdata • Show schema
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id: 159566
{'conductor': 7728, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '7728.o1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 159567
{'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '7728.o1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 16}
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id: 159568
{'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '7728.o1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 159569
{'conductor': 7728, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '7728.o1', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1715003
{'adelic_gens': [[1, 16, 0, 1], [15, 2, 2478, 2563], [2365, 16, 192, 2261], [384, 5, 691, 2562], [2561, 16, 2560, 17], [5, 4, 2572, 2573], [1, 0, 16, 1], [13, 16, 388, 329], [314, 1927, 2251, 1286]], 'adelic_image': '2576.192.1.?', 'conductor': 7728, 'lmfdb_label': '7728.o1', 'prime': 0}
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id: 37881
{'conductor': 7728, 'elladic_image': '16.48.0.32', 'lmfdb_label': '7728.o1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 7728.o does not appear in ec_padic