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ec_curvedata • Show schema
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{'Ciso': '2448n', 'Clabel': '2448n3', 'Cnumber': 3, 'abc_quality': 1.0315574162602832, 'absD': 80803127771136, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 408, 'ainvs': [0, 0, 0, -249699, -48023710], 'analytic_rank': 1, 'bad_primes': [2, 3, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 2448, 'degree': 12288, 'elladic_images': ['8.48.0.137'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.7429580202554997546440657359', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 15, 'isogeny_degrees': [1, 2, 4], 'jinv': [576615941610337, 27060804], 'lmfdb_iso': '2448.p', 'lmfdb_label': '2448.p2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1734, -27936], 'min_quad_twist_disc': 12, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0.e.1', '12.24.0-4.b.1.3', '24.96.0-8.e.1.5', '136.96.1.?', '408.192.1.?'], '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': '8.0343497823245598031678111908', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.50050469536149959952921099598', 'prec': 103}, 'szpiro_ratio': 6.266496281540907, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, 0, -1, 0, -4, 0], 'aplist': [0, 0, 2, 0, -4, -2, -1, -4, 0, 10, -8, -2, -10, -12, 0, -6, 12, -10, 12, 0, 10, 8, 4, 6, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 2448, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '2448.p', 'trace_hash': 1538785435641431420}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.030625691201991347690030299438', 'prec': 107}, 'conductor': 2448, 'gens': [[-35065, 29770, 11]], 'heights': [{'__RealLiteral__': 0, 'data': '8.0343497823245598031678111908', 'prec': 100}], 'lmfdb_label': '2448.p2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.21357311248152240761406359795', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.4318421795525965639822134407750288898', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-287, 0, 1], [577, 0, 1]], 'xcoord_integral_points': [-290, -287, 577]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [1, 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': '2448.p2'}
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ec_torsion_growth • Show schema
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id: 125510
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 4]}
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id: 125512
{'degree': 4, 'field': [1, 0, -4, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 4]}
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id: 125511
{'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 4]}
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id: 125517
{'degree': 8, 'field': [-12, 0, 177, 0, 63, 0, -17, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 6]}
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id: 125513
{'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [4, 4]}
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id: 125514
{'degree': 8, 'field': [4, 24, 166, -124, 143, -2, 15, -2, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 8]}
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id: 125516
{'degree': 8, 'field': [9, 0, 12, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 8]}
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id: 125515
{'degree': 8, 'field': [256, 0, -144, 0, 65, 0, -9, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 8]}
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id: 125518
{'degree': 16, 'field': [-18674, 194792, 26556, -338360, -62586, 201888, 44824, -68072, -14025, 14792, 2392, -2232, -174, 224, -12, -8, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 8]}
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id: 125520
{'degree': 16, 'field': [1, 0, -4, 0, 8, 0, -24, 0, 47, 0, -24, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [4, 8]}
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id: 125521
{'degree': 16, 'field': [3721, 0, 3065, 0, 742, 0, 479, 0, 682, 0, 407, 0, 118, 0, 17, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [2, 12]}
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id: 125519
{'degree': 16, 'field': [65536, 0, 0, 0, -12544, 0, 0, 0, 2145, 0, 0, 0, -49, 0, 0, 0, 1], 'lmfdb_label': '2448.p2', 'torsion': [4, 8]}
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ec_localdata • Show schema
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id: 41877
{'conductor': 2448, 'conductor_valuation': 4, 'discriminant_valuation': 14, 'j_denominator_valuation': 2, 'kodaira_symbol': -10, 'lmfdb_label': '2448.p2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 41878
{'conductor': 2448, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '2448.p2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 41879
{'conductor': 2448, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '2448.p2', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1679878
{'adelic_gens': [[271, 0, 0, 407], [139, 246, 366, 115], [241, 144, 12, 169], [1, 0, 8, 1], [407, 366, 0, 305], [5, 4, 404, 405], [401, 8, 400, 9], [1, 8, 0, 1]], 'adelic_image': '408.192.1.?', 'conductor': 2448, 'lmfdb_label': '2448.p2', 'prime': 0}
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id: 12107
{'conductor': 2448, 'elladic_image': '8.48.0.137', 'lmfdb_label': '2448.p2', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 75394
{'lmfdb_iso': '2448.p', 'p': 5, 'prec': 20, 'unit': 1774226430238, 'val': 1}
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id: 75401
{'lmfdb_iso': '2448.p', 'p': 11, 'prec': 20, 'unit': 57250848248025176333, 'val': 1}
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id: 75399
{'lmfdb_iso': '2448.p', 'p': 13, 'prec': 20, 'unit': 921861889820929935031, 'val': 1}
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id: 75402
{'lmfdb_iso': '2448.p', 'p': 19, 'prec': 20, 'unit': 495039285642591839228534, 'val': 1}
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id: 75398
{'lmfdb_iso': '2448.p', 'p': 29, 'prec': 20, 'unit': 5305100445640011528626506962, 'val': 1}
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id: 75395
{'lmfdb_iso': '2448.p', 'p': 31, 'prec': 20, 'unit': 21167955518629585536228021950, 'val': 1}
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id: 75408
{'lmfdb_iso': '2448.p', 'p': 37, 'prec': 20, 'unit': 285595912928634975108876757193, 'val': 1}
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id: 75396
{'lmfdb_iso': '2448.p', 'p': 41, 'prec': 20, 'unit': 2665833358689486505587775638713, 'val': 1}
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id: 75397
{'lmfdb_iso': '2448.p', 'p': 43, 'prec': 20, 'unit': 9327799234365198183948134107951, 'val': 1}
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id: 75403
{'lmfdb_iso': '2448.p', 'p': 53, 'prec': 20, 'unit': 331000859338879297918577156524880, 'val': 1}
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id: 75406
{'lmfdb_iso': '2448.p', 'p': 59, 'prec': 20, 'unit': 1241741273932923986789934575236985, 'val': 1}
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id: 75407
{'lmfdb_iso': '2448.p', 'p': 61, 'prec': 20, 'unit': 2416233209694400760369394259603408, 'val': 1}
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id: 75393
{'lmfdb_iso': '2448.p', 'p': 67, 'prec': 20, 'unit': 31960215400315397725296472760511561, 'val': 1}
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id: 75404
{'lmfdb_iso': '2448.p', 'p': 73, 'prec': 20, 'unit': 165773366720971281245560483407047119, 'val': 1}
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id: 75400
{'lmfdb_iso': '2448.p', 'p': 79, 'prec': 20, 'unit': 713100317882009038802900079487890917, 'val': 1}
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id: 75392
{'lmfdb_iso': '2448.p', 'p': 83, 'prec': 20, 'unit': 2765838474621030719325871488938186250, 'val': 1}
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id: 75405
{'lmfdb_iso': '2448.p', 'p': 89, 'prec': 20, 'unit': 3782640173672948886978909104635662889, 'val': 1}
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id: 75391
{'lmfdb_iso': '2448.p', 'p': 97, 'prec': 20, 'unit': 26325447968743833702328113770301641270, 'val': 1}