-
ec_curvedata • Show schema
Hide schema
{'Ciso': '448b', 'Clabel': '448b4', 'Cnumber': 4, 'abc_quality': 1.1170620055320515, 'absD': 314703872, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 56, 'ainvs': [0, 0, 0, -236, 1104], 'analytic_rank': 1, 'bad_primes': [2, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 448, 'degree': 128, 'elladic_images': ['8.24.0.49'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.34454076348138516636207252373', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [11090466, 2401], 'lmfdb_iso': '448.e', 'lmfdb_label': '448.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, -59, -138], 'min_quad_twist_disc': -8, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.k.1.2', '56.48.0-56.v.1.6'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 9, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.0691085767972255605925653628', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.63741774231187068864567298167', 'prec': 107}, 'szpiro_ratio': 4.587395081474694, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
-
ec_classdata • Show schema
Hide schema
{'anlist': [0, 1, 0, 0, 0, -2, 0, 1, 0, -3, 0, -4, 0, -2, 0, 0, 0, -6, 0, 8, 0], 'aplist': [0, 0, -2, 1, -4, -2, -6, 8, 0, -6, -8, 2, 2, -4, 8, -6, 0, 6, -4, 8, 10, -16, 8, -6, -6], 'class_deg': 4, 'class_size': 4, 'conductor': 448, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '448.e', 'trace_hash': 823669738576213693}
-
ec_mwbsd • Show schema
Hide schema
{'area': {'__RealLiteral__': 0, 'data': '0.50203696478935907640370311072', 'prec': 103}, 'conductor': 448, 'gens': [[5, 7, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.0691085767972255605925653628', 'prec': 100}], 'lmfdb_label': '448.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.6236666926210273234649262972', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.7358759869411248186869537580981290600', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[26, 112, 1]], 'xcoord_integral_points': [-16, -6, 5, 12, 26]}
-
ec_iwasawa • Show schema
Hide schema
{'iwdata': {'2': 'a', '3': [3, 1, 0], '5': [1, 0], '7': [2, 0], '11': [1, 0], '13': [3, 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, 0]}, 'iwp0': 0, 'lmfdb_label': '448.e2'}
-
ec_torsion_growth • Show schema
Hide schema
-
id: 19773
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '448.e2', 'torsion': [2, 4]}
-
id: 19774
{'degree': 4, 'field': [2, 0, -8, 0, 1], 'lmfdb_label': '448.e2', 'torsion': [8]}
-
id: 19778
{'degree': 8, 'field': [-3, 0, -6, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '448.e2', 'torsion': [12]}
-
id: 19776
{'degree': 8, 'field': [1, 0, -12, 0, 24, 0, -12, 0, 1], 'lmfdb_label': '448.e2', 'torsion': [2, 8]}
-
id: 19775
{'degree': 8, 'field': [1, 0, -4, 0, 8, 0, -4, 0, 1], 'lmfdb_label': '448.e2', 'torsion': [4, 4]}
-
id: 19777
{'degree': 8, 'field': [1, 0, 2, 0, 10, 0, 2, 0, 1], 'lmfdb_label': '448.e2', 'torsion': [2, 8]}
-
id: 19779
{'degree': 16, 'field': [1, 0, -120, 0, 2044, 0, -3864, 0, 1400, 0, -168, 0, 28, 0, -8, 0, 1], 'lmfdb_label': '448.e2', 'torsion': [16]}
-
id: 19780
{'degree': 16, 'field': [49, 0, -196, 0, 196, 0, -172, 0, 214, 0, 20, 0, 4, 0, -4, 0, 1], 'lmfdb_label': '448.e2', 'torsion': [2, 12]}
-
ec_localdata • Show schema
Hide schema
-
id: 4766
{'conductor': 448, 'conductor_valuation': 6, 'discriminant_valuation': 17, 'j_denominator_valuation': 0, 'kodaira_symbol': -11, 'lmfdb_label': '448.e2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
-
id: 4767
{'conductor': 448, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '448.e2', 'prime': 7, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
-
ec_galrep • Show schema
Hide schema
-
id: 1667764
{'adelic_gens': [[17, 8, 12, 33], [49, 8, 48, 9], [1, 0, 8, 1], [13, 20, 30, 43], [1, 4, 4, 17], [7, 6, 50, 51], [32, 55, 29, 42], [1, 8, 0, 1]], 'adelic_image': '56.48.0.?', 'conductor': 448, 'lmfdb_label': '448.e2', 'prime': 0}
-
id: 1956
{'conductor': 448, 'elladic_image': '8.24.0.49', 'lmfdb_label': '448.e2', 'modell_image': '2B', 'prime': 2}
-
ec_padic • Show schema
Hide schema
-
id: 6478
{'lmfdb_iso': '448.e', 'p': 5, 'prec': 20, 'unit': 3939248071437, 'val': 1}
-
id: 6477
{'lmfdb_iso': '448.e', 'p': 11, 'prec': 20, 'unit': 11519404534210648913, 'val': 1}
-
id: 6484
{'lmfdb_iso': '448.e', 'p': 13, 'prec': 20, 'unit': 365542586286747368, 'val': 2}
-
id: 6486
{'lmfdb_iso': '448.e', 'p': 17, 'prec': 20, 'unit': 168563034468757130639783, 'val': 1}
-
id: 6487
{'lmfdb_iso': '448.e', 'p': 19, 'prec': 20, 'unit': 416687839586044907793264, 'val': 1}
-
id: 6483
{'lmfdb_iso': '448.e', 'p': 29, 'prec': 20, 'unit': 2334525100792377250577648914, 'val': 1}
-
id: 6480
{'lmfdb_iso': '448.e', 'p': 31, 'prec': 20, 'unit': 8628857519371855149483063307, 'val': 1}
-
id: 6494
{'lmfdb_iso': '448.e', 'p': 37, 'prec': 20, 'unit': 572837885068115837556818355955, 'val': 1}
-
id: 6481
{'lmfdb_iso': '448.e', 'p': 41, 'prec': 20, 'unit': 616637057558985056696426256558, 'val': 1}
-
id: 6482
{'lmfdb_iso': '448.e', 'p': 43, 'prec': 20, 'unit': 7378368516595481848709355449452, 'val': 1}
-
id: 6485
{'lmfdb_iso': '448.e', 'p': 47, 'prec': 20, 'unit': 9865327354091872377620303707323, 'val': 1}
-
id: 6488
{'lmfdb_iso': '448.e', 'p': 53, 'prec': 20, 'unit': 388741426325728983392299547761374, 'val': 1}
-
id: 6493
{'lmfdb_iso': '448.e', 'p': 61, 'prec': 20, 'unit': 6352285742564239659485056642618488, 'val': 1}
-
id: 6476
{'lmfdb_iso': '448.e', 'p': 67, 'prec': 20, 'unit': 2836162561630575471828131497005109, 'val': 1}
-
id: 6479
{'lmfdb_iso': '448.e', 'p': 71, 'prec': 20, 'unit': 62527083443691607759237056129787032, 'val': 1}
-
id: 6489
{'lmfdb_iso': '448.e', 'p': 73, 'prec': 20, 'unit': 186878963408208825531874772054464258, 'val': 1}
-
id: 6492
{'lmfdb_iso': '448.e', 'p': 79, 'prec': 20, 'unit': 982570524121878337435774619093099832, 'val': 1}
-
id: 6490
{'lmfdb_iso': '448.e', 'p': 83, 'prec': 20, 'unit': 1078742382337335011397340721762669611, 'val': 1}
-
id: 6491
{'lmfdb_iso': '448.e', 'p': 89, 'prec': 20, 'unit': 10837656028004276466243448156450853250, 'val': 1}
-
id: 6475
{'lmfdb_iso': '448.e', 'p': 97, 'prec': 20, 'unit': 39166778048282752111881749239156730603, 'val': 1}