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ec_curvedata • Show schema
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{'Ciso': '8400bt', 'Clabel': '8400bt1', 'Cnumber': 1, 'abc_quality': 0.9636830884406813, 'absD': 13934592000, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 420, 'ainvs': [0, -1, 0, -2728, -53648], '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': '0.78449378435906422736080968021', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 29, 'isogeny_degrees': [1, 2], 'jinv': [4386781853, 27216], 'lmfdb_iso': '8400.bd', 'lmfdb_label': '8400.bd1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -171, 838], 'min_quad_twist_disc': -4, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.b.1', '84.6.0.?', '210.6.0.?', '420.12.0.?'], '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': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.31101287430940617570661227455', 'prec': 107}, 'szpiro_ratio': 3.9119070994096368, '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, 2, 0, -2, 0, 0, 0, -8, 0, 2, 0], 'aplist': [0, -1, 0, 1, 2, -2, -8, 2, 0, -6, -6, -8, 6, 8, 4, 2, 8, 10, -12, 14, 10, -4, 16, 10, -10], 'class_deg': 2, 'class_size': 2, 'conductor': 8400, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '8400.bd', 'trace_hash': 1562548198646284450}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.20825592046860876630226016506', 'prec': 103}, 'conductor': 8400, 'gens': [], 'heights': [], 'lmfdb_label': '8400.bd1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.66082657582764877878326493249', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3216531516552975575665298649759035058', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-28, 0, 1]], 'xcoord_integral_points': [-28]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [0, 0], '5': 'a', '7': [3, 0]}, 'iwp0': 3, 'lmfdb_label': '8400.bd1'}
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ec_torsion_growth • Show schema
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id: 439349
{'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '8400.bd1', 'torsion': [2, 2]}
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id: 439350
{'degree': 4, 'field': [6, 2, -1, -2, 1], 'lmfdb_label': '8400.bd1', 'torsion': [4]}
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id: 439353
{'degree': 8, 'field': [-5054, 12046, -10961, 4992, -1341, 204, 1, -2, 1], 'lmfdb_label': '8400.bd1', 'torsion': [6]}
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id: 439351
{'degree': 8, 'field': [-89, -420, -662, -420, -81, 0, -8, 0, 1], 'lmfdb_label': '8400.bd1', 'torsion': [2, 4]}
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id: 439352
{'degree': 8, 'field': [576, 0, 69, 0, -89, 0, 19, 0, 1], 'lmfdb_label': '8400.bd1', 'torsion': [2, 4]}
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id: 439354
{'degree': 16, 'field': [1296, -5184, 7488, -3744, -348, -240, 1672, -1472, 900, -352, 12, 0, 57, -44, 18, -4, 1], 'lmfdb_label': '8400.bd1', 'torsion': [8]}
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id: 439355
{'degree': 16, 'field': [84640000, 0, 142760000, 0, -75488000, 0, 12026000, 0, -683900, 0, -70000, 0, 280, 0, 5, 0, 1], 'lmfdb_label': '8400.bd1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 175034
{'conductor': 8400, 'conductor_valuation': 4, 'discriminant_valuation': 16, 'j_denominator_valuation': 4, 'kodaira_symbol': -12, 'lmfdb_label': '8400.bd1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 175035
{'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 5, 'j_denominator_valuation': 5, 'kodaira_symbol': 9, 'lmfdb_label': '8400.bd1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 175036
{'conductor': 8400, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '8400.bd1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 175037
{'conductor': 8400, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '8400.bd1', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1719443
{'adelic_gens': [[109, 316, 104, 315], [1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [62, 1, 179, 0], [417, 4, 416, 5], [142, 1, 139, 0], [88, 1, 83, 0]], 'adelic_image': '420.12.0.?', 'conductor': 8400, 'lmfdb_label': '8400.bd1', 'prime': 0}
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id: 41041
{'conductor': 8400, 'elladic_image': '2.3.0.1', 'lmfdb_label': '8400.bd1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 8400.bd does not appear in ec_padic