-
ec_curvedata • Show schema
Hide schema
{'Ciso': '12321c', 'Clabel': '12321c1', 'Cnumber': 1, 'abc_quality': 0.8826782160855301, 'absD': 69205338429957, 'adelic_genus': 43, 'adelic_index': 1296, 'adelic_level': 1998, 'ainvs': [0, 0, 1, -41070, -3178476], 'analytic_rank': 0, 'bad_primes': [3, 37], 'class_deg': 9, 'class_size': 3, 'cm': 0, 'conductor': 12321, 'degree': 27360, 'elladic_images': ['27.36.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.4782343715117607314932102226', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 5, 'isogeny_degrees': [1, 3, 9], 'jinv': [4096000, 37], 'lmfdb_iso': '12321.f', 'lmfdb_label': '12321.f3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 1, -3, 1], 'min_quad_twist_disc': -111, 'modell_images': ['3B'], 'modm_images': ['3.4.0.a.1', '6.8.0-3.a.1.2', '9.12.0.a.1', '18.24.0-9.a.1.2', '27.36.0.a.1', '54.72.0-27.a.1.1', '74.2.0.?', '111.8.0.?', '222.16.0.?', '333.72.0.?', '666.144.3.?', '999.648.16.?', '1998.1296.43.?'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[3, 2, 1369], [37, 722, 9]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.87653072914440633638846023138', 'prec': 107}, 'szpiro_ratio': 4.616458626962283, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
-
ec_classdata • Show schema
Hide schema
{'anlist': [0, 1, 0, 0, -2, 0, 0, -1, 0, 0, 0, -3, 0, 4, 0, 0, 4, 6, 0, -2, 0], 'aplist': [0, 0, 0, -1, -3, 4, 6, -2, 6, -6, 4, 0, 9, -8, -3, 3, 12, -8, -4, 15, 11, 10, -9, 6, -8], 'class_deg': 9, 'class_size': 3, 'conductor': 12321, 'isogeny_matrix': [[1, 3, 9], [3, 1, 3], [9, 3, 1]], 'lmfdb_iso': '12321.f', 'trace_hash': 1819177559694568828}
-
ec_mwbsd • Show schema
Hide schema
{'area': {'__RealLiteral__': 0, 'data': '0.052002226551280991024380524306', 'prec': 107}, 'conductor': 12321, 'gens': [], 'heights': [], 'lmfdb_label': '12321.f3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.33554836020596701074061932227', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3421934408238680429624772890700738727', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [], 'xcoord_integral_points': []}
-
ec_iwasawa • Show schema
Hide schema
{'iwdata': {'2': 's?', '3': 'a', '5': [0, 0, 0], '7': [0, 0], '11': [0, 0], '13': [0, 0], '17': [0, 0], '19': [0, 0], '23': [0, 0], '29': [0, 0], '31': [0, 0], '37': 'a', '41': [0, 0], '43': [0, 0], '47': [0, 0]}, 'iwp0': 0, 'lmfdb_label': '12321.f3'}
-
ec_torsion_growth • Show schema
Hide schema
-
id: 635209
{'degree': 2, 'field': [28, -1, 1], 'lmfdb_label': '12321.f3', 'torsion': [3]}
-
id: 635210
{'degree': 3, 'field': [1, -3, -1, 1], 'lmfdb_label': '12321.f3', 'torsion': [2]}
-
id: 635212
{'degree': 6, 'field': [-37, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '12321.f3', 'torsion': [3]}
-
id: 635211
{'degree': 6, 'field': [1, -5, 0, 9, -2, -3, 1], 'lmfdb_label': '12321.f3', 'torsion': [2, 2]}
-
id: 635214
{'degree': 6, 'field': [58, -38, 28, -19, 13, -3, 1], 'lmfdb_label': '12321.f3', 'torsion': [6]}
-
id: 635213
{'degree': 6, 'field': [184, 36, 52, -83, 22, -1, 1], 'lmfdb_label': '12321.f3', 'torsion': [9]}
-
id: 635218
{'degree': 12, 'field': [1, -5, 25, -18, 47, -23, 68, -23, 31, -12, 11, -3, 1], 'lmfdb_label': '12321.f3', 'torsion': [2, 6]}
-
id: 635215
{'degree': 12, 'field': [382, 1784, -240, -1956, -1868, -672, 8, 240, -48, -26, -4, 0, 1], 'lmfdb_label': '12321.f3', 'torsion': [4]}
-
id: 635217
{'degree': 12, 'field': [469, 634, 642, 389, -182, -239, 51, 55, -13, 6, 2, -2, 1], 'lmfdb_label': '12321.f3', 'torsion': [9]}
-
id: 635216
{'degree': 12, 'field': [1296, 216, 576, -1530, 645, 96, 67, -126, 90, -50, 21, -6, 1], 'lmfdb_label': '12321.f3', 'torsion': [3, 3]}
-
id: 635219
{'degree': 18, 'field': [-1553, -19137, 934, -24069, 11055, -1330, -8225, 11855, 7171, 4092, 2689, -271, -103, -70, -119, -11, -10, -3, 1], 'lmfdb_label': '12321.f3', 'torsion': [2, 6]}
-
id: 635220
{'degree': 18, 'field': [45907, 261258, 683658, 980738, 1065541, 949934, 728309, 430294, 197627, 74286, 29184, 9972, 2652, 850, 329, 2, 31, -2, 1], 'lmfdb_label': '12321.f3', 'torsion': [18]}
-
ec_localdata • Show schema
Hide schema
-
id: 266024
{'conductor': 12321, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '12321.f3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
-
id: 266025
{'conductor': 12321, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '12321.f3', 'prime': 37, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
-
ec_galrep • Show schema
Hide schema
-
id: 1745666
{'adelic_gens': [[31, 36, 172, 1231], [1, 54, 0, 1], [1436, 1989, 985, 1208], [1, 0, 54, 1], [1741, 723, 1025, 686], [1945, 54, 1944, 55], [28, 27, 729, 703]], 'adelic_image': '1998.1296.43.?', 'conductor': 12321, 'lmfdb_label': '12321.f3', 'prime': 0}
-
id: 58661
{'conductor': 12321, 'elladic_image': '27.36.0.1', 'lmfdb_label': '12321.f3', 'modell_image': '3B', 'prime': 3}
-
lmfdb_iso 12321.f does not appear in ec_padic
