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ec_curvedata • Show schema
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{'Ciso': '8400bx', 'Clabel': '8400bx2', 'Cnumber': 2, 'abc_quality': 0.8134635874817913, 'absD': 73500000000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 420, 'ainvs': [0, -1, 0, -1708, 24412], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 8400, 'degree': 7680, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.81273440261996626629858081148', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2], 'jinv': [1102736, 147], 'lmfdb_iso': '8400.o', 'lmfdb_label': '8400.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -68, -168], 'min_quad_twist_disc': -20, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '60.6.0.a.1', '84.6.0.?', '140.6.0.?', '420.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, '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': '-0.85644215207890588759681010274', 'prec': 107}, 'szpiro_ratio': 3.7564710568662347, '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, 0, 0, 1, 0, 1, 0, -4, 0, -2, 0, 0, 0, -2, 0, 2, 0], 'aplist': [0, -1, 0, 1, -4, -2, -2, 2, -6, 6, -6, 4, 0, -4, 4, 2, -4, -2, -12, 8, -14, -16, 16, 16, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 8400, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '8400.o', 'trace_hash': 1409486051160630396}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.19681938361413524937408033180', 'prec': 103}, 'conductor': 8400, 'gens': [], 'heights': [], 'lmfdb_label': '8400.o1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.0508986578861542240935936085', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0508986578861542240935936085126982222', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[17, 0, 1]], 'xcoord_integral_points': [17]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [0, 0], '5': 'a', '7': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '8400.o1'}
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ec_torsion_growth • Show schema
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id: 439402
{'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '8400.o1', 'torsion': [2, 2]}
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id: 439403
{'degree': 4, 'field': [135, 0, 20, 0, 1], 'lmfdb_label': '8400.o1', 'torsion': [4]}
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id: 439406
{'degree': 8, 'field': [-5054, 12046, -10961, 4992, -1341, 204, 1, -2, 1], 'lmfdb_label': '8400.o1', 'torsion': [6]}
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id: 439404
{'degree': 8, 'field': [36, 0, -72, 0, 84, 0, -48, 0, 1], 'lmfdb_label': '8400.o1', 'torsion': [2, 4]}
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id: 439405
{'degree': 8, 'field': [1521, -1638, 2022, -810, 511, -130, 48, -4, 1], 'lmfdb_label': '8400.o1', 'torsion': [2, 4]}
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id: 439408
{'degree': 16, 'field': [-17101784, 68905172, -68268907, -1631308, 1726998, -1135372, 452107, -70358, 24639, -1550, -2935, 1874, -373, 0, 20, -8, 1], 'lmfdb_label': '8400.o1', 'torsion': [2, 6]}
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id: 439407
{'degree': 16, 'field': [159668496, 0, -8250336, 0, -153360, 0, 76176, 0, 25884, 0, -264, 0, -60, 0, 4, 0, 1], 'lmfdb_label': '8400.o1', 'torsion': [8]}
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ec_localdata • Show schema
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id: 175066
{'conductor': 8400, 'conductor_valuation': 4, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '8400.o1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 175067
{'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8400.o1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 175068
{'conductor': 8400, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '8400.o1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 175069
{'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '8400.o1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1719587
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [316, 109, 105, 316], [1, 2, 2, 5], [1, 4, 0, 1], [417, 4, 416, 5], [142, 1, 139, 0], [88, 1, 83, 0], [241, 4, 62, 9]], 'adelic_image': '420.12.0.?', 'conductor': 8400, 'lmfdb_label': '8400.o1', 'prime': 0}
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id: 41189
{'conductor': 8400, 'elladic_image': '2.3.0.1', 'lmfdb_label': '8400.o1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 8400.o does not appear in ec_padic