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ec_curvedata • Show schema
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{'Ciso': '27735g', 'Clabel': '27735g5', 'Cnumber': 5, 'abc_quality': 1.0558519748642754, 'absD': 22223541969140625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 20640, 'ainvs': [1, 0, 1, 64676, 3376247], 'analytic_rank': 1, 'bad_primes': [3, 5, 43], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 27735, 'degree': 161280, 'elladic_images': ['8.48.0.197'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8248960760439100790014408202', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4733169839, 3515625], 'lmfdb_iso': '27735.k', 'lmfdb_label': '27735.k8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 35, -28], 'min_quad_twist_disc': -43, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0.n.2', '24.96.1.cv.2', '80.96.1.?', '160.192.5.?', '172.24.0.?', '240.192.5.?', '344.96.0.?', '480.384.13.?', '1032.192.1.?', '3440.192.1.?', '6880.384.5.?', '10320.384.5.?', '20640.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '12.963289798892616851885377353', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436474', 'prec': 110}, 'szpiro_ratio': 4.3834884848253965, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 1, -1, -1, 1, 0, -3, 1, -1, -4, -1, -2, 0, -1, -1, 2, 1, -4, 1], 'aplist': [1, 1, -1, 0, -4, -2, 2, -4, 0, 2, 0, 10, 10, 0, 8, -10, -4, 2, 12, 8, -10, 0, 12, 6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 27735, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '27735.k', 'trace_hash': 512768579550082875}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.025996531542064291881008637001', 'prec': 107}, 'conductor': 27735, 'gens': [[12775519, 54653658487, 182]], 'heights': [{'__RealLiteral__': 0, 'data': '12.963289798892616851885377353', 'prec': 100}], 'lmfdb_label': '27735.k8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.24342465677963694852701872385', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '6.3111687400608082795801419247052479412', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-201, 197, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 1], '3': [4, 0], '5': [1, 0], '7': [3, 1, 0], '11': [1, 0], '13': [1, 0], '17': [3, 0], '19': [3, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': 'a', '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '27735.k8'}
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ec_torsion_growth • Show schema
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id: 1388051
{'degree': 2, 'field': [-43, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [4]}
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id: 1388050
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [2, 2]}
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id: 1388052
{'degree': 2, 'field': [11, -1, 1], 'lmfdb_label': '27735.k8', 'torsion': [8]}
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id: 1388053
{'degree': 4, 'field': [121, 0, -21, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [2, 8]}
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id: 1388054
{'degree': 4, 'field': [1369, 0, -98, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [8]}
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id: 1388055
{'degree': 4, 'field': [2401, 0, -74, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [8]}
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id: 1388058
{'degree': 8, 'field': [-40059, 360, -11787, 429, -498, -28, -3, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [6]}
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id: 1388057
{'degree': 8, 'field': [6964, -5960, 6746, -1622, 937, -154, 56, -4, 1], 'lmfdb_label': '27735.k8', 'torsion': [16]}
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id: 1388056
{'degree': 8, 'field': [16513, -4172, 4916, -1532, 877, -136, 50, -4, 1], 'lmfdb_label': '27735.k8', 'torsion': [4, 8]}
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id: 1388061
{'degree': 16, 'field': [13792561, -112189320, 288018316, -252128640, 50416180, 48071760, -25179116, -628320, 3285829, -293280, -234296, 17400, 9250, -240, -164, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [16]}
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id: 1388064
{'degree': 16, 'field': [178302609, 0, -131595291, 0, 43247880, 0, -8078167, 0, 937385, 0, -69577, 0, 3235, 0, -86, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [12]}
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id: 1388065
{'degree': 16, 'field': [178302609, 0, 131595291, 0, 43247880, 0, 8078167, 0, 937385, 0, 69577, 0, 3235, 0, 86, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [24]}
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id: 1388060
{'degree': 16, 'field': [200385901, 168033838, -69735756, -69267582, 20314670, 14760268, -4589658, -1976962, 653139, 169204, -56022, -8962, 2834, 270, -78, -4, 1], 'lmfdb_label': '27735.k8', 'torsion': [2, 16]}
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id: 1388059
{'degree': 16, 'field': [223242244, -153439592, 201542420, -105003736, 75510006, -30520408, 15251182, -4816364, 1808625, -441816, 128434, -23500, 5312, -672, 116, -8, 1], 'lmfdb_label': '27735.k8', 'torsion': [2, 16]}
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id: 1388063
{'degree': 16, 'field': [1604723481, 0, -944221266, 0, 178523253, 0, -11816325, 0, 262632, 0, 21370, 0, -987, 0, 6, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [2, 6]}
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id: 1388062
{'degree': 16, 'field': [6550482290881, 0, -1533953135912, 0, 146918211928, 0, -7715210480, 0, 248129806, 0, -4880600, 0, 57208, 0, -368, 0, 1], 'lmfdb_label': '27735.k8', 'torsion': [16]}
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ec_localdata • Show schema
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id: 640635
{'conductor': 27735, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '27735.k8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 640636
{'conductor': 27735, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '27735.k8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 640637
{'conductor': 27735, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '27735.k8', 'prime': 43, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1848963
{'adelic_gens': [[13933, 4816, 9374, 345], [14105, 9632, 8342, 2409], [1, 0, 32, 1], [1, 32, 4, 129], [25, 16, 18904, 19529], [8257, 2408, 0, 1], [5759, 0, 0, 20639], [17287, 4816, 7095, 11353], [1, 32, 0, 1], [20609, 32, 20608, 33]], 'adelic_image': '20640.768.13.?', 'conductor': 27735, 'lmfdb_label': '27735.k8', 'prime': 0}
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id: 125379
{'conductor': 27735, 'elladic_image': '8.48.0.197', 'lmfdb_label': '27735.k8', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 1329049
{'lmfdb_iso': '27735.k', 'p': 11, 'prec': 20, 'unit': 40879464271524253180, 'val': 1}
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id: 1329051
{'lmfdb_iso': '27735.k', 'p': 13, 'prec': 20, 'unit': 678262326205482375468, 'val': 1}
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id: 1329053
{'lmfdb_iso': '27735.k', 'p': 17, 'prec': 20, 'unit': 526300767743413471817, 'val': 2}
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id: 1329054
{'lmfdb_iso': '27735.k', 'p': 19, 'prec': 20, 'unit': 34863066262508768535404, 'val': 2}
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id: 1329050
{'lmfdb_iso': '27735.k', 'p': 29, 'prec': 20, 'unit': 3047112413454121642194924457, 'val': 1}
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id: 1329046
{'lmfdb_iso': '27735.k', 'p': 37, 'prec': 20, 'unit': 482398635338791802518811947572, 'val': 1}
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id: 1329048
{'lmfdb_iso': '27735.k', 'p': 41, 'prec': 20, 'unit': 3506072121479282151539931611332, 'val': 1}
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id: 1329052
{'lmfdb_iso': '27735.k', 'p': 47, 'prec': 20, 'unit': 40842158126065742497012224916256, 'val': 1}
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id: 1329055
{'lmfdb_iso': '27735.k', 'p': 53, 'prec': 20, 'unit': 529786011144410565264530981581755, 'val': 1}
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id: 1329058
{'lmfdb_iso': '27735.k', 'p': 59, 'prec': 20, 'unit': 4083378574535776479445180751821056, 'val': 1}
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id: 1329059
{'lmfdb_iso': '27735.k', 'p': 61, 'prec': 20, 'unit': 5685758835835201915873174819220861, 'val': 1}
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id: 1329045
{'lmfdb_iso': '27735.k', 'p': 67, 'prec': 20, 'unit': 18989583067876005321428817399227445, 'val': 1}
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id: 1329047
{'lmfdb_iso': '27735.k', 'p': 71, 'prec': 20, 'unit': 22732089217265808909403927395867202, 'val': 1}
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id: 1329056
{'lmfdb_iso': '27735.k', 'p': 73, 'prec': 20, 'unit': 130101805959184543590563070677240547, 'val': 1}
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id: 1329044
{'lmfdb_iso': '27735.k', 'p': 83, 'prec': 20, 'unit': 401887033779570119442062354822300236, 'val': 1}
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id: 1329057
{'lmfdb_iso': '27735.k', 'p': 89, 'prec': 20, 'unit': 991397941110913322190808719816039010, 'val': 1}
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id: 1329043
{'lmfdb_iso': '27735.k', 'p': 97, 'prec': 20, 'unit': 33960474489626684930375542515154904903, 'val': 1}