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ec_curvedata • Show schema
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{'Ciso': '53361bo', 'Clabel': '53361bo3', 'Cnumber': 3, 'abc_quality': 1.0015974661127929, 'absD': 6978144480103329687, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 3696, 'ainvs': [1, -1, 1, -2082191, -1148929680], 'analytic_rank': 0, 'bad_primes': [3, 7, 11], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 53361, 'degree': 983040, 'elladic_images': ['8.24.0.88'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4488406483718638863309205731', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [6570725617, 45927], 'lmfdb_iso': '53361.p', 'lmfdb_label': '53361.p3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -39, 90], 'min_quad_twist_disc': -231, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0.bb.1', '28.12.0.h.1', '48.48.0.bf.1', '56.48.0.bl.2', '132.12.0.?', '176.48.0.?', '264.48.0.?', '336.96.1.?', '528.96.0.?', '924.24.0.?', '1232.96.0.?', '1848.96.0.?', '3696.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.27236820688903288395035020607', 'prec': 107}, 'szpiro_ratio': 5.076824245190555, '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, 0, 3, 0, 2, 0, 0, -2, 0, 0, -1, 6, 0, 4, 2], 'aplist': [-1, 0, -2, 0, 0, -2, 6, 4, 0, -2, 0, 6, -2, 4, 0, -6, 12, -2, 4, 0, -6, 16, 12, -14, -18], 'class_deg': 8, 'class_size': 6, 'conductor': 53361, 'isogeny_matrix': [[1, 2, 8, 4, 4, 8], [2, 1, 4, 2, 2, 4], [8, 4, 1, 8, 2, 4], [4, 2, 8, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], 'lmfdb_iso': '53361.p', 'trace_hash': 1235016221343198693}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0074638695206677660661139157324', 'prec': 110}, 'conductor': 53361, 'gens': [], 'heights': [], 'lmfdb_label': '53361.p3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.12573389652964633421550109159', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0058711722371706737240087327313882978', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-3541, 3537, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'o?', '3': 'a', '7': 'a', '11': 'a'}, 'iwp0': 3, 'lmfdb_label': '53361.p3'}
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ec_torsion_growth • Show schema
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id: 2584075
{'degree': 2, 'field': [-7, 0, 1], 'lmfdb_label': '53361.p3', 'torsion': [2, 2]}
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id: 2584076
{'degree': 2, 'field': [33, 0, 1], 'lmfdb_label': '53361.p3', 'torsion': [4]}
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id: 2584077
{'degree': 2, 'field': [58, -1, 1], 'lmfdb_label': '53361.p3', 'torsion': [8]}
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id: 2584078
{'degree': 4, 'field': [100, 0, 13, 0, 1], 'lmfdb_label': '53361.p3', 'torsion': [2, 8]}
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id: 2584082
{'degree': 8, 'field': [-4759, -3143, 6133, -3089, 809, -127, 44, -2, 1], 'lmfdb_label': '53361.p3', 'torsion': [6]}
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id: 2584081
{'degree': 8, 'field': [2704, 0, -1536, 0, 311, 0, -27, 0, 1], 'lmfdb_label': '53361.p3', 'torsion': [16]}
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id: 2584079
{'degree': 8, 'field': [3018, 2748, -2378, -708, 275, 92, -26, -4, 1], 'lmfdb_label': '53361.p3', 'torsion': [2, 4]}
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id: 2584080
{'degree': 8, 'field': [1247689, 0, 132660, 0, 6590, 0, 132, 0, 1], 'lmfdb_label': '53361.p3', 'torsion': [8]}
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id: 2584085
{'degree': 16, 'field': [12769, 16498, 34198, -3536, 19769, 3814, 3030, 1870, -244, 812, -264, 62, 41, -28, 16, -4, 1], 'lmfdb_label': '53361.p3', 'torsion': [2, 16]}
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id: 2584086
{'degree': 16, 'field': [1515361, 0, -2660112, 0, 634558, 0, -224513, 0, 30825, 0, -6035, 0, 625, 0, -9, 0, 1], 'lmfdb_label': '53361.p3', 'torsion': [2, 6]}
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id: 2584084
{'degree': 16, 'field': [6232788, -3292488, 4328628, -2246328, 1586914, -637448, 350210, -125100, 43177, -12496, 6622, -1708, -140, 168, -4, -8, 1], 'lmfdb_label': '53361.p3', 'torsion': [2, 16]}
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id: 2584083
{'degree': 16, 'field': [9108324, 0, 21905112, 0, 11205952, 0, 2471732, 0, 357573, 0, 33184, 0, 1962, 0, 68, 0, 1], 'lmfdb_label': '53361.p3', 'torsion': [4, 8]}
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id: 2584087
{'degree': 16, 'field': [13638249, 0, 20184804, 0, 10960936, 0, 2822043, 0, 375900, 0, 31969, 0, 1869, 0, 66, 0, 1], 'lmfdb_label': '53361.p3', 'torsion': [12]}
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id: 2584088
{'degree': 16, 'field': [168703539, -138367248, 126740757, 61007679, 7481631, 5320176, 3037372, -155488, 551858, -108372, 57698, -9962, 3351, -458, 101, -8, 1], 'lmfdb_label': '53361.p3', 'torsion': [24]}
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ec_localdata • Show schema
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id: 1280605
{'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '53361.p3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1280606
{'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '53361.p3', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 1280607
{'conductor': 53361, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '53361.p3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 2018790
{'adelic_gens': [[3112, 671, 1793, 2342], [1, 16, 0, 1], [5, 4, 3692, 3693], [1231, 3344, 440, 879], [1, 352, 1100, 1893], [2234, 935, 715, 1398], [3681, 16, 3680, 17], [1, 0, 16, 1], [3023, 0, 0, 3695], [15, 2, 3598, 3683]], 'adelic_image': '3696.192.1.?', 'conductor': 53361, 'lmfdb_label': '53361.p3', 'prime': 0}
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id: 228090
{'conductor': 53361, 'elladic_image': '8.24.0.88', 'lmfdb_label': '53361.p3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 53361.p does not appear in ec_padic