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ec_curvedata • Show schema
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{'Ciso': '161a', 'Clabel': '161a4', 'Cnumber': 4, 'abc_quality': 0.9793224770887127, 'absD': 1958887, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 1288, 'ainvs': [1, -1, 1, 26, 36], 'analytic_rank': 0, 'bad_primes': [7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 161, 'degree': 20, 'elladic_images': ['4.12.0.8'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.10563384719344526212878020275', 'prec': 107}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [2014698447, 1958887], 'lmfdb_iso': '161.a', 'lmfdb_label': '161.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, 26, 36], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '14.6.0.b.1', '28.24.0-28.g.1.1', '184.24.0.?', '1288.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.10563384719344526212878020275', 'prec': 107}, 'szpiro_ratio': 4.216105200105833, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, -1, 2, 0, 1, 3, -3, -2, 4, 0, 6, -1, 0, -1, -2, 3, 4, -2], 'aplist': [-1, 0, 2, 1, 4, 6, -2, 4, -1, -2, -4, -2, -6, 12, -12, -10, 0, 2, 12, 8, -14, 8, -4, 6, -10], 'class_deg': 4, 'class_size': 4, 'conductor': 161, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '161.a', 'trace_hash': 990649218870667461}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.2352429784181801025508190732', 'prec': 100}, 'conductor': 161, 'gens': [], 'heights': [], 'lmfdb_label': '161.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.7256686535952035235407514591', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.86283432679760176177037572955874819882', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[-5, 1, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 1], '7': [3, 0], '23': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '161.a4'}
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ec_torsion_growth • Show schema
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id: 6398
{'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [4]}
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id: 6399
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [4]}
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id: 6397
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '161.a4', 'torsion': [2, 2]}
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id: 6401
{'degree': 4, 'field': [2, -4, 3, -1, 1], 'lmfdb_label': '161.a4', 'torsion': [2, 4]}
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id: 6400
{'degree': 4, 'field': [4, 0, -3, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [2, 4]}
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id: 6405
{'degree': 8, 'field': [-3, 0, 15, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [6]}
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id: 6402
{'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '161.a4', 'torsion': [4, 4]}
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id: 6404
{'degree': 8, 'field': [196, 0, 88, 0, 72, 0, 20, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [8]}
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id: 6403
{'degree': 8, 'field': [25921, 0, -9016, 0, 462, 0, -56, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [8]}
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id: 6406
{'degree': 16, 'field': [4, 0, 2952, 0, 3648, 0, 900, 0, 837, 0, 116, 0, -2, 0, 8, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [2, 8]}
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id: 6408
{'degree': 16, 'field': [49, 0, 0, 0, -392, 0, 0, 0, 945, 0, 0, 0, 56, 0, 0, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [2, 8]}
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id: 6411
{'degree': 16, 'field': [49, 0, 98, 0, 49, 0, 1304, 0, 694, 0, 50, 0, 16, 0, 8, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [12]}
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id: 6409
{'degree': 16, 'field': [2304, 0, 8640, 0, 14688, 0, 4320, 0, 669, 0, 135, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [2, 6]}
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id: 6410
{'degree': 16, 'field': [110889, 0, 148716, 0, -178470, 0, -21852, 0, 8619, 0, 1164, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '161.a4', 'torsion': [12]}
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id: 6407
{'degree': 16, 'field': [851008, 1404352, -755536, -1269520, 566538, 76076, -15302, -10460, 7281, -6924, 5446, -2548, 728, -168, 44, -8, 1], 'lmfdb_label': '161.a4', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 1233
{'conductor': 161, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '161.a4', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 1234
{'conductor': 161, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '161.a4', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1666425
{'adelic_gens': [[491, 484, 530, 1133], [1, 0, 8, 1], [1281, 8, 1280, 9], [1, 8, 0, 1], [281, 8, 1124, 33], [1, 4, 4, 17], [1131, 1130, 818, 171], [7, 6, 1282, 1283], [192, 3, 925, 2]], 'adelic_image': '1288.48.0.?', 'conductor': 161, 'lmfdb_label': '161.a4', 'prime': 0}
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id: 629
{'conductor': 161, 'elladic_image': '4.12.0.8', 'lmfdb_label': '161.a4', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 161.a does not appear in ec_padic