-
ec_curvedata • Show schema
Hide schema
{'Ciso': '56a', 'Clabel': '56a1', 'Cnumber': 1, 'abc_quality': 0.8915192755066496, 'absD': 1792, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 56, 'ainvs': [0, 0, 0, 1, 2], 'analytic_rank': 0, 'bad_primes': [2, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 56, 'degree': 2, 'elladic_images': ['8.24.0.50'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.69518000735853279776377565845', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4], 'jinv': [432, 7], 'lmfdb_iso': '56.a', 'lmfdb_label': '56.a4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 1, 2], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.p.1.1', '14.6.0.b.1', '28.24.0-28.g.1.2', '56.48.0-56.bn.1.6'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1572781277318296707085970728', 'prec': 103}, 'szpiro_ratio': 3.7038850376835257, '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': 56, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '56.a', 'trace_hash': 1158293942075606764}
-
ec_mwbsd • Show schema
Hide schema
{'area': {'__RealLiteral__': 0, 'data': '4.0162957183148726112296248857', 'prec': 100}, 'conductor': 56, 'gens': [], 'heights': [], 'lmfdb_label': '56.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.4981932567533454612034413989', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.87454831418833636530086034972735623668', 'prec': 133}, 'tamagawa_product': 4, 'torsion_generators': [[1, 2, 1]], 'xcoord_integral_points': [-1, 1]}
-
ec_iwasawa • Show schema
Hide schema
{'iwdata': {'2': 'a', '7': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '56.a4'}
-
ec_torsion_growth • Show schema
Hide schema
-
id: 1943
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '56.a4', 'torsion': [2, 4]}
-
id: 1944
{'degree': 4, 'field': [-2, -4, -2, 0, 1], 'lmfdb_label': '56.a4', 'torsion': [8]}
-
id: 1948
{'degree': 8, 'field': [1, -4, 4, 2, -8, 2, 4, -4, 1], 'lmfdb_label': '56.a4', 'torsion': [12]}
-
id: 1945
{'degree': 8, 'field': [1, -2, 2, 4, -1, 4, 2, -2, 1], 'lmfdb_label': '56.a4', 'torsion': [4, 4]}
-
id: 1946
{'degree': 8, 'field': [1, 0, -10, 0, 34, 0, -10, 0, 1], 'lmfdb_label': '56.a4', 'torsion': [2, 8]}
-
id: 1947
{'degree': 8, 'field': [1, 0, 2, 0, 10, 0, 2, 0, 1], 'lmfdb_label': '56.a4', 'torsion': [2, 8]}
-
id: 1949
{'degree': 16, 'field': [4, 32, 96, 144, 152, 192, 216, 128, 36, 16, -16, -56, -44, -16, -4, 0, 1], 'lmfdb_label': '56.a4', 'torsion': [16]}
-
id: 1950
{'degree': 16, 'field': [9, 0, -36, 0, 324, 0, -72, 0, 30, 0, 12, 0, -12, 0, 0, 0, 1], 'lmfdb_label': '56.a4', 'torsion': [2, 12]}
-
ec_localdata • Show schema
Hide schema
-
id: 276
{'conductor': 56, 'conductor_valuation': 3, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -5, 'lmfdb_label': '56.a4', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
-
id: 277
{'conductor': 56, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '56.a4', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
-
ec_galrep • Show schema
Hide schema
-
id: 1666020
{'adelic_gens': [[43, 38, 26, 51], [25, 24, 6, 31], [49, 8, 48, 9], [24, 3, 29, 2], [1, 0, 8, 1], [1, 4, 4, 17], [7, 6, 50, 51], [1, 8, 0, 1]], 'adelic_image': '56.48.0.?', 'conductor': 56, 'lmfdb_label': '56.a4', 'prime': 0}
-
id: 173
{'conductor': 56, 'elladic_image': '8.24.0.50', 'lmfdb_label': '56.a4', 'modell_image': '2B', 'prime': 2}
-
lmfdb_iso 56.a does not appear in ec_padic