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ec_curvedata • Show schema
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{'Ciso': '85680ds', 'Clabel': '85680ds4', 'Cnumber': 4, 'abc_quality': 1.105043631919779, 'absD': 42961732430400000000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 2856, 'ainvs': [0, 0, 0, -880563, -41282638], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 85680, 'degree': 2097152, 'elladic_images': ['8.24.0.18'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4570883619881151064461501891', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 4], 'jinv': [25288177725059761, 14387797265625], 'lmfdb_iso': '85680.g', 'lmfdb_label': '85680.g2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -6115, -24400], 'min_quad_twist_disc': 12, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.1', '12.24.0-4.b.1.3', '24.48.0-8.e.1.9', '28.24.0-4.b.1.2', '56.48.0-8.e.1.16', '84.48.0.?', '136.48.0.?', '168.96.0.?', '408.96.0.?', '952.96.0.?', '2856.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.0305152633809090978502081433', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.2146350370941149513312954492', 'prec': 100}, 'szpiro_ratio': 4.637860139691753, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -4, 0, -2, 0, 0, 0, -1, 0, 4, 0], 'aplist': [0, 0, -1, -1, -4, -2, -1, 4, -8, -6, 0, -10, 6, 4, 0, -6, -4, 6, -4, 8, 2, 16, -12, 6, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 85680, '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': '85680.g', 'trace_hash': 1805986434642798549}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0073417596997678854174623824763', 'prec': 110}, 'conductor': 85680, 'gens': [[-551, 16632, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.0305152633809090978502081433', 'prec': 100}], 'lmfdb_label': '85680.g2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.16844458855358150197996567697', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.0837911731643672906275594496128025911', 'prec': 130}, 'tamagawa_product': 128, 'torsion_generators': [[-47, 0, 1], [961, 0, 1]], 'xcoord_integral_points': [-914, -551, -289, -47, 961, 1687]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 0], '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '85680.g2'}
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ec_torsion_growth • Show schema
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id: 4015727
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 4]}
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id: 4015728
{'degree': 4, 'field': [1, 0, -5, 0, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 4]}
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id: 4015729
{'degree': 4, 'field': [22, 2, -1, -2, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 4]}
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id: 4015734
{'degree': 8, 'field': [-6627, 0, 3210, 0, 423, 0, 22, 0, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 6]}
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id: 4015730
{'degree': 8, 'field': [16, 0, 12, 0, 5, 0, 3, 0, 1], 'lmfdb_label': '85680.g2', 'torsion': [4, 4]}
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id: 4015733
{'degree': 8, 'field': [25, -10, -62, -106, -77, 2, 4, -4, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 8]}
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id: 4015732
{'degree': 8, 'field': [6561, 0, -1296, 0, 175, 0, -16, 0, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 8]}
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id: 4015731
{'degree': 8, 'field': [24700, -10120, 7792, -1672, 1407, -86, 67, -2, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 8]}
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id: 4015737
{'degree': 16, 'field': [9, 0, 1299, 0, 187471, 0, 2598, 0, 39, 0, 866, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 12]}
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id: 4015736
{'degree': 16, 'field': [625, 250, 50, 1320, -211, -682, 1138, -474, -20, 228, -152, 46, 5, -12, 8, -4, 1], 'lmfdb_label': '85680.g2', 'torsion': [4, 8]}
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id: 4015735
{'degree': 16, 'field': [1092025, 0, -632072, 0, 2154226, 0, -240716, 0, -27197, 0, 2884, 0, 478, 0, 28, 0, 1], 'lmfdb_label': '85680.g2', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 2089733
{'conductor': 85680, 'conductor_valuation': 4, 'discriminant_valuation': 12, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '85680.g2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 2089734
{'conductor': 85680, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '85680.g2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 2089735
{'conductor': 85680, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '85680.g2', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 2089736
{'conductor': 85680, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '85680.g2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 2089737
{'conductor': 85680, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '85680.g2', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 2228392
{'adelic_gens': [[5, 4, 2852, 2853], [1, 0, 8, 1], [2689, 8, 2188, 33], [7, 6, 402, 2851], [1433, 716, 736, 1437], [1897, 2850, 6, 5], [2849, 2136, 2834, 695], [2849, 8, 2848, 9], [1, 8, 0, 1]], 'adelic_image': '2856.192.1.?', 'conductor': 85680, 'lmfdb_label': '85680.g2', 'prime': 0}
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id: 349636
{'conductor': 85680, 'elladic_image': '8.24.0.18', 'lmfdb_label': '85680.g2', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 4422885
{'lmfdb_iso': '85680.g', 'p': 11, 'prec': 20, 'unit': 39086364787273692409, 'val': 1}
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id: 4422883
{'lmfdb_iso': '85680.g', 'p': 13, 'prec': 20, 'unit': 105669327413897495111, 'val': 2}
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id: 4422886
{'lmfdb_iso': '85680.g', 'p': 19, 'prec': 20, 'unit': 1343920267342314540055731, 'val': 1}
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id: 4422889
{'lmfdb_iso': '85680.g', 'p': 23, 'prec': 20, 'unit': 5798269086231382271527640, 'val': 1}
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id: 4422882
{'lmfdb_iso': '85680.g', 'p': 29, 'prec': 20, 'unit': 637230086847387650376378899, 'val': 1}
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id: 4422878
{'lmfdb_iso': '85680.g', 'p': 37, 'prec': 20, 'unit': 202347434087820901150293073508, 'val': 1}
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id: 4422880
{'lmfdb_iso': '85680.g', 'p': 41, 'prec': 20, 'unit': 3782274571856499005726259013013, 'val': 1}
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id: 4422881
{'lmfdb_iso': '85680.g', 'p': 43, 'prec': 20, 'unit': 2215804362863772140510569054221, 'val': 1}
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id: 4422887
{'lmfdb_iso': '85680.g', 'p': 53, 'prec': 20, 'unit': 326959061196951647716545729669727, 'val': 1}
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id: 4422891
{'lmfdb_iso': '85680.g', 'p': 59, 'prec': 20, 'unit': 2820884960114844892473311859988549, 'val': 1}
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id: 4422892
{'lmfdb_iso': '85680.g', 'p': 61, 'prec': 20, 'unit': 4112996486903312192060503242403302, 'val': 1}
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id: 4422877
{'lmfdb_iso': '85680.g', 'p': 67, 'prec': 20, 'unit': 24170622131958506151465973845541209, 'val': 1}
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id: 4422879
{'lmfdb_iso': '85680.g', 'p': 71, 'prec': 20, 'unit': 110445723314400586026933322541549715, 'val': 1}
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id: 4422888
{'lmfdb_iso': '85680.g', 'p': 73, 'prec': 20, 'unit': 182160032547857047677930890309859366, 'val': 1}
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id: 4422884
{'lmfdb_iso': '85680.g', 'p': 79, 'prec': 20, 'unit': 154475389958848824115824481742805333, 'val': 1}
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id: 4422876
{'lmfdb_iso': '85680.g', 'p': 83, 'prec': 20, 'unit': 2716385866049678008728396928479698240, 'val': 1}
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id: 4422890
{'lmfdb_iso': '85680.g', 'p': 89, 'prec': 20, 'unit': 830159633240676177521999246901627993, 'val': 1}
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id: 4422875
{'lmfdb_iso': '85680.g', 'p': 97, 'prec': 20, 'unit': 14546701020341867397795355206296519123, 'val': 1}