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ec_curvedata • Show schema
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{'Ciso': '520a', 'Clabel': '520a4', 'Cnumber': 4, 'abc_quality': 0.9522581122514642, 'absD': 292464640, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 520, 'ainvs': [0, 0, 0, 157, -322], 'analytic_rank': 1, 'bad_primes': [2, 5, 13], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 520, 'degree': 128, 'elladic_images': ['8.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.31312067564260852407659768065', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [208974222, 142805], 'lmfdb_iso': '520.a', 'lmfdb_label': '520.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 157, -322], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0-4.c.1.4', '20.12.0-4.c.1.1', '40.24.0-40.s.1.4', '104.24.0.?', '520.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.8012626368254185049286360095', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.32226423987067467622253176402', 'prec': 107}, 'szpiro_ratio': 4.282550938905786, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, -1, 0, 0, 0, -3, 0, -4, 0, -1, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, -1, 0, -4, -1, -6, 4, 0, -2, -4, -6, -6, 8, 0, 2, 4, -10, 12, -4, 14, -16, 12, 2, -2], 'class_deg': 4, 'class_size': 4, 'conductor': 520, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '520.a', 'trace_hash': 82918068213281691}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.53459739329253256465686095928', 'prec': 103}, 'conductor': 520, 'gens': [[38, 246, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.8012626368254185049286360095', 'prec': 100}], 'lmfdb_label': '520.a4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.98015427442971718522424807505', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.8629119108572058100196073275625378692', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[2, 0, 1]], 'xcoord_integral_points': [2, 38]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [1, 0], '7': [1, 1, 0], '11': [3, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '520.a4'}
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ec_torsion_growth • Show schema
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id: 23314
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [4]}
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id: 23315
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [4]}
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id: 23313
{'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [2, 2]}
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id: 23316
{'degree': 4, 'field': [9, 0, 4, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [2, 4]}
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id: 23320
{'degree': 8, 'field': [-48, 0, -144, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [6]}
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id: 23317
{'degree': 8, 'field': [171, -156, 182, -48, 15, 8, 2, -4, 1], 'lmfdb_label': '520.a4', 'torsion': [2, 4]}
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id: 23318
{'degree': 8, 'field': [484, 0, -304, 0, 100, 0, -24, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [8]}
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id: 23319
{'degree': 8, 'field': [1681, -492, 33, -34, 110, -4, -7, -2, 1], 'lmfdb_label': '520.a4', 'torsion': [8]}
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id: 23321
{'degree': 16, 'field': [625, 0, 0, 0, 0, 0, 0, 0, 850, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [4, 4]}
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id: 23325
{'degree': 16, 'field': [2209, 0, -13396, 0, 8200, 0, -2872, 0, 1030, 0, -532, 0, 100, 0, -16, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [12]}
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id: 23322
{'degree': 16, 'field': [6561, 0, -10368, 0, 21488, 0, -18080, 0, 7426, 0, -1920, 0, 368, 0, -32, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [2, 8]}
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id: 23326
{'degree': 16, 'field': [59049, 0, -157464, 0, 233280, 0, -34992, 0, 3390, 0, -792, 0, 12, 0, 0, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [12]}
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id: 23323
{'degree': 16, 'field': [141376, 0, 186304, 0, 127280, 0, 52496, 0, 13844, 0, 2456, 0, 300, 0, 24, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [2, 8]}
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id: 23324
{'degree': 16, 'field': [47499664, 0, -2362816, 0, -567200, 0, 71792, 0, 14920, 0, -928, 0, -68, 0, 20, 0, 1], 'lmfdb_label': '520.a4', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 5787
{'conductor': 520, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '520.a4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 5788
{'conductor': 520, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '520.a4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 5789
{'conductor': 520, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '520.a4', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1668124
{'adelic_gens': [[41, 8, 164, 33], [513, 8, 512, 9], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [216, 3, 5, 2], [328, 73, 187, 174], [7, 6, 514, 515], [456, 203, 459, 488]], 'adelic_image': '520.48.0.?', 'conductor': 520, 'lmfdb_label': '520.a4', 'prime': 0}
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id: 2312
{'conductor': 520, 'elladic_image': '8.12.0.8', 'lmfdb_label': '520.a4', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 8114
{'lmfdb_iso': '520.a', 'p': 11, 'prec': 20, 'unit': 323179995244294938, 'val': 3}
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id: 8115
{'lmfdb_iso': '520.a', 'p': 17, 'prec': 20, 'unit': 153405655041912116515232, 'val': 1}
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id: 8116
{'lmfdb_iso': '520.a', 'p': 19, 'prec': 20, 'unit': 1698241839303449278224276, 'val': 1}
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id: 8112
{'lmfdb_iso': '520.a', 'p': 29, 'prec': 20, 'unit': 2424850319667219127164876954, 'val': 1}
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id: 8122
{'lmfdb_iso': '520.a', 'p': 31, 'prec': 20, 'unit': 13266137882473047657237946932, 'val': 1}
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id: 8108
{'lmfdb_iso': '520.a', 'p': 37, 'prec': 20, 'unit': 86135211635021909279392883571, 'val': 1}
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id: 8110
{'lmfdb_iso': '520.a', 'p': 41, 'prec': 20, 'unit': 1329839150863811297654916333828, 'val': 1}
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id: 8111
{'lmfdb_iso': '520.a', 'p': 43, 'prec': 20, 'unit': 7298734575947547335671611065386, 'val': 1}
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id: 8117
{'lmfdb_iso': '520.a', 'p': 53, 'prec': 20, 'unit': 410695981268171397496113855464145, 'val': 1}
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id: 8120
{'lmfdb_iso': '520.a', 'p': 59, 'prec': 20, 'unit': 2194985894659288914140723030418927, 'val': 1}
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id: 8121
{'lmfdb_iso': '520.a', 'p': 61, 'prec': 20, 'unit': 5143182155492476725231029488792110, 'val': 1}
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id: 8107
{'lmfdb_iso': '520.a', 'p': 67, 'prec': 20, 'unit': 29692527750084647974368561386608479, 'val': 1}
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id: 8109
{'lmfdb_iso': '520.a', 'p': 71, 'prec': 20, 'unit': 29670987417261413061431676292099360, 'val': 1}
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id: 8118
{'lmfdb_iso': '520.a', 'p': 73, 'prec': 20, 'unit': 10859218723850148375837697522281815, 'val': 1}
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id: 8113
{'lmfdb_iso': '520.a', 'p': 79, 'prec': 20, 'unit': 1123735196522221914170897240183552891, 'val': 1}
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id: 8106
{'lmfdb_iso': '520.a', 'p': 83, 'prec': 20, 'unit': 1153051239103930365892404273938598187, 'val': 1}
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id: 8119
{'lmfdb_iso': '520.a', 'p': 89, 'prec': 20, 'unit': 1670957342734853766016841753946322080, 'val': 1}
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id: 8105
{'lmfdb_iso': '520.a', 'p': 97, 'prec': 20, 'unit': 16968142478539324220127201316337039290, 'val': 1}