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ec_curvedata • Show schema
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{'Ciso': '242550nk', 'Clabel': '242550nk4', 'Cnumber': 4, 'abc_quality': 0.9957188233471589, 'absD': 143059170669060514089375000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 9240, 'ainvs': [1, -1, 1, -826996505, 9135946998497], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7, 11], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 242550, 'degree': 127401984, 'elladic_images': ['4.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.9000956619461366047780096953', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 348, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [46676570542430835889, 106752955783320], 'lmfdb_iso': '242550.nk', 'lmfdb_label': '242550.nk4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -75011, 7885545], 'min_quad_twist_disc': 105, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '12.24.0.g.1', '24.48.0-12.g.1.18', '60.48.0-12.g.1.3', '84.48.0.?', '88.12.0.?', '105.8.0.?', '120.96.0.?', '168.96.0.?', '210.24.0.?', '264.96.0.?', '280.12.0.?', '420.96.0.?', '840.192.1.?', '1320.192.1.?', '1848.192.1.?', '3080.24.0.?', '9240.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2133552458011997908549392421', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.5731154868673749192273310385', 'prec': 100}, 'szpiro_ratio': 5.904811168866257, '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, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, -6, 0, 4, 0], 'aplist': [1, 0, 0, 0, 1, 2, -6, 4, 0, -6, -8, 10, -6, -8, 0, 6, 12, -2, 4, -12, -10, -4, 12, 6, -10], 'class_deg': 12, 'class_size': 8, 'conductor': 242550, 'isogeny_matrix': [[1, 4, 2, 12, 3, 4, 6, 12], [4, 1, 2, 3, 12, 4, 6, 12], [2, 2, 1, 6, 6, 2, 3, 6], [12, 3, 6, 1, 4, 12, 2, 4], [3, 12, 6, 4, 1, 12, 2, 4], [4, 4, 2, 12, 12, 1, 6, 3], [6, 6, 3, 2, 2, 6, 1, 2], [12, 12, 6, 4, 4, 3, 2, 1]], 'lmfdb_iso': '242550.nk', 'trace_hash': 259632372536344053}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.00040965659438746956671770135259', 'prec': 113}, 'conductor': 242550, 'gens': [[-18891, 4254070, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2133552458011997908549392421', 'prec': 100}], 'lmfdb_label': '242550.nk4', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.058196467371676384010849941853', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '12.365707809043035502054297942437239283', 'prec': 130}, 'tamagawa_product': 384, 'torsion_generators': [[68811, -68815, 2]], 'xcoord_integral_points': [-18891]}
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lmfdb_label 242550.nk4 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 10465461
{'degree': 2, 'field': [-70, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 2]}
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id: 10465462
{'degree': 2, 'field': [-42, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [4]}
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id: 10465464
{'degree': 2, 'field': [-26, -1, 1], 'lmfdb_label': '242550.nk4', 'torsion': [6]}
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id: 10465463
{'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [4]}
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id: 10465468
{'degree': 4, 'field': [4, 0, -11, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [12]}
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id: 10465465
{'degree': 4, 'field': [49, 0, -56, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 4]}
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id: 10465467
{'degree': 4, 'field': [64, 0, -26, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [12]}
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id: 10465466
{'degree': 4, 'field': [256, 0, -38, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 6]}
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id: 10465469
{'degree': 6, 'field': [5184, -3048, 105, 55, 30, -3, 1], 'lmfdb_label': '242550.nk4', 'torsion': [6]}
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id: 10465473
{'degree': 8, 'field': [576, 0, -912, 0, 313, 0, -32, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 12]}
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id: 10465470
{'degree': 8, 'field': [73896, -12576, 12112, 912, -415, -52, 22, -4, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 4]}
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id: 10465472
{'degree': 8, 'field': [182329, 0, -11466, 0, 602, 0, -42, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [8]}
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id: 10465471
{'degree': 8, 'field': [1488400, 0, -200800, 0, 8910, 0, -160, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [8]}
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id: 10465474
{'degree': 12, 'field': [142884, 0, 655263, 0, 86095, 0, 14975, 0, 1125, 0, 53, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [3, 6]}
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id: 10465477
{'degree': 12, 'field': [8503056, 0, 323676, 0, 94365, 0, -2475, 0, -620, 0, 1, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [12]}
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id: 10465475
{'degree': 12, 'field': [45965196, -34895256, 6983376, 1490800, -463185, -79086, 43181, -5106, 1290, -130, 81, -6, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 6]}
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id: 10465476
{'degree': 12, 'field': [544195584, 0, -10357632, 0, 1509840, 0, 19800, 0, -2480, 0, -2, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [12]}
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id: 10465478
{'degree': 16, 'field': [40271716, 0, 40821872, 0, 13071188, 0, 1140384, 0, -48115, 0, -756, 0, 638, 0, -28, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [4, 4]}
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id: 10465479
{'degree': 16, 'field': [67650625, 0, -49599620000, 0, 24801103000, 0, -3735749000, 0, 223795150, 0, -5859200, 0, 73720, 0, -440, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 8]}
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id: 10465483
{'degree': 16, 'field': [281568400, 0, 78630780, 0, 58995709, 0, 5957919, 0, 1225299, 0, 50598, 0, 2551, 0, 39, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [24]}
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id: 10465481
{'degree': 16, 'field': [6186395296, 768930496, -658710064, -214637136, 93152878, 16038176, -3748416, -1365968, 345003, -14624, 15456, -7168, 1498, -168, 44, -8, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 12]}
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id: 10465480
{'degree': 16, 'field': [12990528576, 0, -1806482304, 0, 10792224, 0, 110784, 0, 1602004, 0, -165224, 0, 6504, 0, -116, 0, 1], 'lmfdb_label': '242550.nk4', 'torsion': [2, 8]}
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id: 10465482
{'degree': 16, 'field': [84947034096, 149069154816, -111385628064, -71671386816, 26771870898, 10389989376, -2665374336, -658062048, 132547783, 20681776, -3511784, -333728, 49858, 2632, -356, -8, 1], 'lmfdb_label': '242550.nk4', 'torsion': [24]}
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id: 10465484
{'degree': 18, 'field': [195328885479141, -239925136681170, 101134405148841, -13490981469636, -2752819318620, 1338798129228, -181158050828, -14207734212, 8064905862, -745126280, -87270642, 26206740, -1309692, -339948, 39060, 2164, -339, -6, 1], 'lmfdb_label': '242550.nk4', 'torsion': [18]}
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ec_localdata • Show schema
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id: 6012338
{'conductor': 242550, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '242550.nk4', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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id: 6012339
{'conductor': 242550, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '242550.nk4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 6012340
{'conductor': 242550, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '242550.nk4', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 6012341
{'conductor': 242550, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 3, 'kodaira_symbol': -7, 'lmfdb_label': '242550.nk4', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 6012342
{'conductor': 242550, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '242550.nk4', 'prime': 11, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 3205683
{'adelic_gens': [[4619, 9216, 6148, 7411], [1, 12, 12, 145], [15, 106, 7934, 11], [6934, 3, 6975, 34], [1926, 409, 4235, 2696], [2521, 24, 2532, 289], [5528, 9237, 6003, 86], [9217, 24, 9216, 25], [7904, 9219, 8205, 374], [1, 24, 0, 1], [1, 0, 24, 1]], 'adelic_image': '9240.384.5.?', 'conductor': 242550, 'lmfdb_label': '242550.nk4', 'prime': 0}
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id: 878323
{'conductor': 242550, 'elladic_image': '4.6.0.1', 'lmfdb_label': '242550.nk4', 'modell_image': '2B', 'prime': 2}
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id: 878324
{'conductor': 242550, 'elladic_image': '3.4.0.1', 'lmfdb_label': '242550.nk4', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 242550.nk does not appear in ec_padic