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ec_curvedata • Show schema
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{'Ciso': '1680j', 'Clabel': '1680j1', 'Cnumber': 1, 'abc_quality': 0.9605836908258326, 'absD': 8400, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 1680, 'ainvs': [0, 1, 0, -175, -952], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 1680, 'degree': 256, 'elladic_images': ['8.24.0.55'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.10680569706124191930461182873', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 19, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [37256083456, 525], 'lmfdb_iso': '1680.t', 'lmfdb_label': '1680.t4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -175, 952], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.24.0-8.n.1.6', '42.6.0.a.1', '48.48.0-48.e.2.7', '80.48.0.?', '84.24.0.?', '112.48.0.?', '120.48.0.?', '168.48.0.?', '240.96.0.?', '280.48.0.?', '336.96.0.?', '560.96.0.?', '840.96.0.?', '1680.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.33785475724789035577702253588', 'prec': 107}, 'szpiro_ratio': 3.6509110140680896, '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, 1, 0, 1, 0, 1, 0, 4, 0, -2, 0, 1, 0, 2, 0, 4, 0], 'aplist': [0, 1, 1, 1, 4, -2, 2, 4, 0, -10, 0, 6, -6, 4, 8, 6, 4, -10, -4, 16, -14, -8, 4, 10, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 1680, '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': '1680.t', 'trace_hash': 1210627288603867288}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.2381414122626690820393506917', 'prec': 100}, 'conductor': 1680, 'gens': [], 'heights': [], 'lmfdb_label': '1680.t4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.3119998926916089654922066638', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.6239997853832179309844133275975858176', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[-8, 0, 1]], 'xcoord_integral_points': [-8]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [5, 0], '5': [1, 0], '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '1680.t4'}
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ec_torsion_growth • Show schema
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id: 84472
{'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '1680.t4', 'torsion': [2, 2]}
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id: 84474
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [4]}
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id: 84473
{'degree': 2, 'field': [21, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [4]}
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id: 84476
{'degree': 4, 'field': [-525, 0, 0, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [2, 4]}
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id: 84478
{'degree': 4, 'field': [16, 0, -7, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [8]}
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id: 84475
{'degree': 4, 'field': [25, 0, 11, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [2, 4]}
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id: 84477
{'degree': 4, 'field': [46, 52, 12, -2, 1], 'lmfdb_label': '1680.t4', 'torsion': [8]}
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id: 84479
{'degree': 4, 'field': [81, 0, -17, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [8]}
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id: 84483
{'degree': 8, 'field': [-3, 0, 92, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [6]}
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id: 84482
{'degree': 8, 'field': [225, 0, 105, 0, 16, 0, -7, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [2, 8]}
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id: 84481
{'degree': 8, 'field': [2209, 94, 2, -194, 103, -10, 8, -4, 1], 'lmfdb_label': '1680.t4', 'torsion': [2, 8]}
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id: 84480
{'degree': 8, 'field': [17161, 262, 2, -530, 271, -10, 8, -4, 1], 'lmfdb_label': '1680.t4', 'torsion': [4, 4]}
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id: 84484
{'degree': 16, 'field': [-6978505775, 10491399700, -6008768400, 1540410200, -122998750, -25965660, 12241180, -4264640, 1418166, -345668, 30688, -336, 1610, -196, -12, -8, 1], 'lmfdb_label': '1680.t4', 'torsion': [2, 8]}
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id: 84489
{'degree': 16, 'field': [9, 0, -25248, 0, -67100, 0, -50496, 0, 30, 0, 8416, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [2, 6]}
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id: 84491
{'degree': 16, 'field': [10000, 0, 20000, 0, 10000, 0, -2976, 0, -2088, 0, 264, 0, 16, 0, 8, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [12]}
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id: 84485
{'degree': 16, 'field': [364816, 82144, 9248, -81888, 123416, -8944, 4048, -13536, 16657, -3954, 466, -26, -25, -18, 8, -4, 1], 'lmfdb_label': '1680.t4', 'torsion': [4, 8]}
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id: 84490
{'degree': 16, 'field': [2490084, 0, 579048, 0, 1138300, 0, 288696, 0, 22080, 0, 184, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '1680.t4', 'torsion': [12]}
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id: 84488
{'degree': 16, 'field': [167987521, 204576424, 124567328, -24328192, 7428736, 7081144, 4876480, -1052776, 126274, 38408, 39200, -10528, 1456, 56, 32, -8, 1], 'lmfdb_label': '1680.t4', 'torsion': [16]}
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id: 84487
{'degree': 16, 'field': [235960321, 108510104, 24950048, 2349168, 880856, 46984, -59840, 96984, -9326, -4392, 160, 752, -184, -24, 32, -8, 1], 'lmfdb_label': '1680.t4', 'torsion': [16]}
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id: 84486
{'degree': 16, 'field': [1280879373, 330511740, 113970432, -47857656, -28591080, -6877920, -952266, 254232, 240571, -8068, 20986, -5740, 1246, -280, 58, -4, 1], 'lmfdb_label': '1680.t4', 'torsion': [16]}
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ec_localdata • Show schema
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id: 26537
{'conductor': 1680, 'conductor_valuation': 4, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '1680.t4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 26538
{'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1680.t4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 26539
{'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '1680.t4', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 26540
{'conductor': 1680, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1680.t4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1675051
{'adelic_gens': [[5, 4, 1676, 1677], [1021, 16, 1088, 1365], [1, 16, 0, 1], [1665, 16, 1664, 17], [1, 16, 420, 421], [15, 2, 1582, 1667], [496, 5, 915, 1666], [568, 1, 1199, 10], [1, 0, 16, 1], [195, 1664, 526, 309]], 'adelic_image': '1680.192.1.?', 'conductor': 1680, 'lmfdb_label': '1680.t4', 'prime': 0}
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id: 8239
{'conductor': 1680, 'elladic_image': '8.24.0.55', 'lmfdb_label': '1680.t4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 1680.t does not appear in ec_padic