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ec_curvedata • Show schema
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{'Ciso': '208080i', 'Clabel': '208080i1', 'Cnumber': 1, 'abc_quality': 1.2368891427142117, 'absD': 16567166290825728000, 'adelic_genus': 0, 'adelic_index': 16, 'adelic_level': 60, 'ainvs': [0, 0, 0, -638112, 11980784], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 17], 'class_deg': 3, 'class_size': 2, 'cm': 0, 'conductor': 208080, 'degree': 3981312, 'elladic_images': ['3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.3773810359797144284864670928', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 116, 'isogeny_degrees': [1, 3], 'jinv': [115220905984, 66430125], 'lmfdb_iso': '208080.em', 'lmfdb_label': '208080.em2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -4431, 5456], 'min_quad_twist_disc': 12, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '10.2.0.a.1', '12.8.0-3.a.1.2', '30.8.0.a.1', '60.16.0-30.a.1.4'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.6696512461419358155236420045', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 13005], [3, 2, 4624], [5, 6, 41616], [17, 114, 720]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.19052326306697557995510081359', 'prec': 103}, 'szpiro_ratio': 4.2229111969974715, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, -5, 0], 'aplist': [0, 0, 1, -2, -3, -4, 0, -5, 0, 3, -8, 2, 3, 10, -6, 6, 15, 5, -2, -15, 2, 1, -6, -9, -10], 'class_deg': 3, 'class_size': 2, 'conductor': 208080, 'isogeny_matrix': [[1, 3], [3, 1]], 'lmfdb_iso': '208080.em', 'trace_hash': 1823682138210868405}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0086105931511306579422814234926', 'prec': 110}, 'conductor': 208080, 'gens': [[-287, 13095, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.6696512461419358155236420045', 'prec': 100}], 'lmfdb_label': '208080.em2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.18708915294497679681062561422', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.2418465771349007210001963782800742155', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [-287]}
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lmfdb_label 208080.em2 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 9099371
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [3]}
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id: 9099372
{'degree': 3, 'field': [5, -11, -1, 1], 'lmfdb_label': '208080.em2', 'torsion': [2]}
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id: 9099375
{'degree': 6, 'field': [-188, -104, 132, 44, -30, -2, 1], 'lmfdb_label': '208080.em2', 'torsion': [6]}
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id: 9099373
{'degree': 6, 'field': [-125, -25, 130, 15, -26, -1, 1], 'lmfdb_label': '208080.em2', 'torsion': [2, 2]}
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id: 9099374
{'degree': 6, 'field': [144, 0, 12, 0, -11, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [3]}
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id: 9099376
{'degree': 12, 'field': [-408735, 1242036, -1104822, 186624, 130783, -30624, -8208, 1824, 443, -84, -18, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [4]}
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id: 9099377
{'degree': 12, 'field': [144, 0, -132, 0, 109, 0, -35, 0, 12, 0, 1, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [3, 3]}
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id: 9099378
{'degree': 12, 'field': [3001, 7408, -20325, -25406, 41646, 12068, -12933, -1894, 1494, 112, -69, -2, 1], 'lmfdb_label': '208080.em2', 'torsion': [2, 6]}
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id: 9099379
{'degree': 18, 'field': [-26343, 79488, -158112, -517728, 1017864, -242460, -568106, 374016, 132834, -169106, -5472, 39132, -3579, -4752, 630, 274, -42, -6, 1], 'lmfdb_label': '208080.em2', 'torsion': [9]}
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id: 9099380
{'degree': 18, 'field': [36, 0, 232, 0, 376, 0, 249, 0, 221, 0, 58, 0, -31, 0, -18, 0, 1, 0, 1], 'lmfdb_label': '208080.em2', 'torsion': [6]}
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ec_localdata • Show schema
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id: 5154987
{'conductor': 208080, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '208080.em2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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id: 5154988
{'conductor': 208080, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '208080.em2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 5154989
{'conductor': 208080, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '208080.em2', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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id: 5154990
{'conductor': 208080, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '208080.em2', 'prime': 17, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2995731
{'adelic_gens': [[1, 0, 6, 1], [4, 3, 9, 7], [53, 54, 39, 41], [3, 4, 8, 11], [54, 59, 35, 39], [55, 6, 54, 7], [35, 54, 36, 53], [29, 0, 0, 59], [1, 6, 0, 1]], 'adelic_image': '60.16.0.?', 'conductor': 208080, 'lmfdb_label': '208080.em2', 'prime': 0}
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id: 768569
{'conductor': 208080, 'elladic_image': '3.4.0.1', 'lmfdb_label': '208080.em2', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 208080.em does not appear in ec_padic