-
ec_curvedata • Show schema
Hide schema
{'Ciso': '75b', 'Clabel': '75b5', 'Cnumber': 5, 'abc_quality': 1.038972011651739, 'absD': 2562890625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 240, 'ainvs': [1, 0, 1, -3376, -75727], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 75, 'degree': 48, 'elladic_images': ['8.96.0.31'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.74901497441417905456539923018', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [272223782641, 164025], 'lmfdb_iso': '75.b', 'lmfdb_label': '75.b2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -135, -660], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.24.0-4.b.1.2', '8.96.0-8.k.1.7', '20.48.0-20.c.1.3', '40.192.1-40.cc.2.5', '48.192.1-48.e.2.9', '80.384.5.?', '240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436433', 'prec': 110}, 'szpiro_ratio': 8.335058910078248, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
-
ec_classdata • Show schema
Hide schema
{'anlist': [0, 1, 1, 1, -1, 0, 1, 0, -3, 1, 0, -4, -1, 2, 0, 0, -1, -2, 1, 4, 0], 'aplist': [1, 1, 0, 0, -4, 2, -2, 4, 0, -2, 0, 10, 10, -4, -8, 10, -4, -2, -12, -8, -10, 0, -12, -6, -2], 'class_deg': 16, 'class_size': 8, 'conductor': 75, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '75.b', 'trace_hash': 1988189362737059693}
-
ec_mwbsd • Show schema
Hide schema
{'area': {'__RealLiteral__': 0, 'data': '0.22357017126175291017667427821', 'prec': 103}, 'conductor': 75, 'gens': [], 'heights': [], 'lmfdb_label': '75.b2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.62636872242974274728715805032', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2527374448594854945743161006323838319', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-33, 16, 1], [67, -34, 1]], 'xcoord_integral_points': [-33, 67]}
-
ec_iwasawa • Show schema
Hide schema
{'iwdata': {'2': [1, 2], '3': [1, 0], '5': 'a'}, 'iwp0': 3, 'lmfdb_label': '75.b2'}
-
ec_torsion_growth • Show schema
Hide schema
-
id: 2672
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 4]}
-
id: 2671
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 4]}
-
id: 2674
{'degree': 4, 'field': [-5, 0, 0, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 8]}
-
id: 2673
{'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [4, 4]}
-
id: 2675
{'degree': 4, 'field': [9, 0, -4, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 8]}
-
id: 2676
{'degree': 8, 'field': [1, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [4, 8]}
-
id: 2678
{'degree': 8, 'field': [1, 2, 2, -10, 11, -10, 8, -4, 1], 'lmfdb_label': '75.b2', 'torsion': [4, 8]}
-
id: 2679
{'degree': 8, 'field': [9, -9, -15, 3, 15, -2, -3, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 6]}
-
id: 2677
{'degree': 8, 'field': [36, 0, -56, 0, 16, 0, 4, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [4, 8]}
-
id: 2680
{'degree': 16, 'field': [1, 0, 0, 0, -36, 0, 0, 0, 646, 0, 0, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [8, 8]}
-
id: 2684
{'degree': 16, 'field': [9, 0, -63, 0, 135, 0, -146, 0, 125, 0, -89, 0, 43, 0, -10, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 12]}
-
id: 2685
{'degree': 16, 'field': [9, 0, 63, 0, 135, 0, 146, 0, 125, 0, 89, 0, 43, 0, 10, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 12]}
-
id: 2681
{'degree': 16, 'field': [25, 0, 0, 0, 350, 0, 0, 0, -360, 0, 0, 0, -25, 0, 0, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 16]}
-
id: 2683
{'degree': 16, 'field': [22500, 0, -60000, 0, 59500, 0, -12000, 0, 3525, 0, -200, 0, 120, 0, 0, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 16]}
-
id: 2682
{'degree': 16, 'field': [50625, 0, -45000, 0, 26500, 0, -12000, 0, 3375, 0, 400, 0, -60, 0, 0, 0, 1], 'lmfdb_label': '75.b2', 'torsion': [2, 16]}
-
ec_localdata • Show schema
Hide schema
-
id: 416
{'conductor': 75, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '75.b2', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
-
id: 417
{'conductor': 75, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '75.b2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
-
ec_galrep • Show schema
Hide schema
-
id: 1666076
{'adelic_gens': [[179, 232, 70, 43], [1, 0, 16, 1], [1, 16, 0, 1], [9, 8, 178, 215], [161, 8, 0, 1], [1, 16, 4, 65], [1, 16, 0, 181], [225, 16, 224, 17]], 'adelic_image': '240.768.13.?', 'conductor': 75, 'lmfdb_label': '75.b2', 'prime': 0}
-
id: 234
{'conductor': 75, 'elladic_image': '8.96.0.31', 'lmfdb_label': '75.b2', 'modell_image': '2Cs', 'prime': 2}
-
lmfdb_iso 75.b does not appear in ec_padic