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ec_curvedata • Show schema
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{'Ciso': '84525ca', 'Clabel': '84525ca2', 'Cnumber': 2, 'abc_quality': 0.8833817054418198, 'absD': 10721178734765625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 9660, 'ainvs': [1, 0, 0, -328938, -72470133], 'analytic_rank': 1, 'bad_primes': [3, 5, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 84525, 'degree': 811008, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9494345382417263171874223819', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 17, 'isogeny_degrees': [1, 2], 'jinv': [2141202151369, 5832225], 'lmfdb_iso': '84525.r', 'lmfdb_label': '84525.r2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -269, 1667], 'min_quad_twist_disc': -35, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '20.12.0-2.a.1.1', '84.12.0.?', '276.12.0.?', '420.24.0.?', '644.12.0.?', '1380.24.0.?', '1932.24.0.?', '3220.24.0.?', '9660.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '6.2588017185267979603374391050', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.17176050749701947733436634356', 'prec': 103}, 'szpiro_ratio': 4.383018245578317, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 1, -1, 0, -1, 0, 3, 1, 0, -4, -1, 2, 0, 0, -1, 6, -1, 4, 0], 'aplist': [-1, 1, 0, 0, -4, 2, 6, 4, -1, 6, -8, -6, -6, -4, 0, 10, 0, -10, 12, -8, 14, 4, 0, -6, 2], 'class_deg': 4, 'class_size': 4, 'conductor': 84525, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '84525.r', 'trace_hash': 370318556366458174}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.020264816448940395864220252921', 'prec': 107}, 'conductor': 84525, 'gens': [[-12293, 92129, 6]], 'heights': [{'__RealLiteral__': 0, 'data': '6.2588017185267979603374391050', 'prec': 100}], 'lmfdb_label': '84525.r2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.19938484026602529660522758044', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.9916407236207609223944246955274595525', 'prec': 130}, 'tamagawa_product': 64, 'torsion_generators': [[-318, 159, 1], [662, -331, 1]], 'xcoord_integral_points': [-318, 662]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [5, 1], '3': [2, 0], '5': 'a', '7': 'a', '11': [1, 0], '13': [3, 0], '17': [1, 0], '19': [1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '84525.r2'}
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ec_torsion_growth • Show schema
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id: 3962502
{'degree': 4, 'field': [16, 0, 13, 0, 1], 'lmfdb_label': '84525.r2', 'torsion': [2, 4]}
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id: 3962503
{'degree': 4, 'field': [196, 0, 133, 0, 1], 'lmfdb_label': '84525.r2', 'torsion': [2, 4]}
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id: 3962504
{'degree': 4, 'field': [1521, 0, -83, 0, 1], 'lmfdb_label': '84525.r2', 'torsion': [2, 4]}
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id: 3962505
{'degree': 8, 'field': [-6747039, 203724, -212688, 17927, -8960, -7, 7, -4, 1], 'lmfdb_label': '84525.r2', 'torsion': [2, 6]}
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id: 3962506
{'degree': 16, 'field': [3671056, 0, 12483976, 0, 14819249, 0, 7314264, 0, 1510400, 0, 144834, 0, 6584, 0, 136, 0, 1], 'lmfdb_label': '84525.r2', 'torsion': [4, 4]}
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id: 3962507
{'degree': 16, 'field': [1070243316, -1209498336, 1731544272, -1087277688, 651247008, -128079408, 40788168, 1931196, -832835, 198172, -5288, -17684, 2098, 364, -32, -8, 1], 'lmfdb_label': '84525.r2', 'torsion': [2, 8]}
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id: 3962509
{'degree': 16, 'field': [163879232400, 0, -8882146800, 0, -1643868440, 0, 80028140, 0, 7086281, 0, -556726, 0, 14951, 0, -226, 0, 1], 'lmfdb_label': '84525.r2', 'torsion': [2, 8]}
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id: 3962508
{'degree': 16, 'field': [998103610624320, -608793900094080, 173169623145600, -32727423833280, 5401124145696, -712646565840, 78440714448, -8495106288, 827026009, -74406508, 7660096, -457756, 52822, -1396, 256, -4, 1], 'lmfdb_label': '84525.r2', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 2059413
{'conductor': 84525, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '84525.r2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 2059414
{'conductor': 84525, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '84525.r2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 2059415
{'conductor': 84525, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '84525.r2', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 2059416
{'conductor': 84525, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '84525.r2', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 2220547
{'adelic_gens': [[1, 0, 4, 1], [9657, 4, 9656, 5], [1, 4, 0, 1], [6899, 9656, 4138, 9651], [3221, 2, 0, 1], [1929, 9658, 1934, 1], [4833, 4, 8, 11], [843, 2, 5878, 9659]], 'adelic_image': '9660.48.0.?', 'conductor': 84525, 'lmfdb_label': '84525.r2', 'prime': 0}
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id: 345173
{'conductor': 84525, 'elladic_image': '2.6.0.1', 'lmfdb_label': '84525.r2', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 4358704
{'lmfdb_iso': '84525.r', 'p': 11, 'prec': 20, 'unit': 22584791487210710132, 'val': 1}
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id: 4358702
{'lmfdb_iso': '84525.r', 'p': 13, 'prec': 20, 'unit': 6439208816926834771, 'val': 2}
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id: 4358705
{'lmfdb_iso': '84525.r', 'p': 17, 'prec': 20, 'unit': 230772526915522184008326, 'val': 1}
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id: 4358706
{'lmfdb_iso': '84525.r', 'p': 19, 'prec': 20, 'unit': 1776956561071620241714549, 'val': 1}
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id: 4358701
{'lmfdb_iso': '84525.r', 'p': 29, 'prec': 20, 'unit': 5405261186546534279234487368, 'val': 1}
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id: 4358711
{'lmfdb_iso': '84525.r', 'p': 31, 'prec': 20, 'unit': 310468689540256431134204125, 'val': 1}
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id: 4358697
{'lmfdb_iso': '84525.r', 'p': 37, 'prec': 20, 'unit': 249882643531594461341617159854, 'val': 1}
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id: 4358699
{'lmfdb_iso': '84525.r', 'p': 41, 'prec': 20, 'unit': 501942519335742980609906536505, 'val': 1}
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id: 4358700
{'lmfdb_iso': '84525.r', 'p': 43, 'prec': 20, 'unit': 8511782284602466806133825246379, 'val': 1}
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id: 4358707
{'lmfdb_iso': '84525.r', 'p': 53, 'prec': 20, 'unit': 508857622022006484655933108545253, 'val': 1}
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id: 4358710
{'lmfdb_iso': '84525.r', 'p': 61, 'prec': 20, 'unit': 795898039401082884359732017860164, 'val': 1}
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id: 4358696
{'lmfdb_iso': '84525.r', 'p': 67, 'prec': 20, 'unit': 39605085289330359070223353600370581, 'val': 1}
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id: 4358698
{'lmfdb_iso': '84525.r', 'p': 71, 'prec': 20, 'unit': 106751719623981670162839008915005301, 'val': 1}
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id: 4358708
{'lmfdb_iso': '84525.r', 'p': 73, 'prec': 20, 'unit': 235661384599846951921363412100787340, 'val': 1}
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id: 4358703
{'lmfdb_iso': '84525.r', 'p': 79, 'prec': 20, 'unit': 648197594492658577315615060417013564, 'val': 1}
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id: 4358709
{'lmfdb_iso': '84525.r', 'p': 89, 'prec': 20, 'unit': 2014661975210747380012270778078356152, 'val': 1}
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id: 4358695
{'lmfdb_iso': '84525.r', 'p': 97, 'prec': 20, 'unit': 31302215452744900092896063375219713248, 'val': 1}