-
ec_nfcurves • Show schema
{'Lvalue': {'__RealLiteral__': 0, 'data': '1.03996534225985', 'prec': 54}, 'abs_disc': 6809, 'ainvs': '-1,-5,0,1;3,5,-1,-1;0,1,0,0;16,8,-45,-22;71,-21,-331,-147', 'analytic_rank': 0, 'bad_primes': ['(w+1)', '(w^3-5*w+1)'], 'base_change': [], 'class_deg': 6, 'class_label': '4.4.6809.1-22.1-b', 'class_size': 4, 'cm': 0, 'cm_type': 0, 'conductor_ideal': '(w^2-3)', 'conductor_label': '22.1', 'conductor_norm': 22, 'conductor_norm_factors': [2, 11], 'degree': 4, 'disc': '(-w^3+2*w^2+7*w-8)', 'equation': '{y}^2+\\left(a^{3}-5a-1\\right){x}{y}+a{y}={x}^{3}+\\left(-a^{3}-a^{2}+5a+3\\right){x}^{2}+\\left(-22a^{3}-45a^{2}+8a+16\\right){x}-147a^{3}-331a^{2}-21a+71', 'field_label': '4.4.6809.1', 'galois_images': ['2B', '3B.1.1'], 'gens': [], 'heights': [], 'iso_label': 'b', 'iso_nlabel': 1, 'isodeg': [1, 2, 3, 6], 'isogeny_matrix': [[1, 6, 2, 3], [6, 1, 3, 2], [2, 3, 1, 6], [3, 2, 6, 1]], 'jinv': '-89719838093/16,365938930215/44,4227375539575/176,-2042536312629/176', 'label': '4.4.6809.1-22.1-b4', 'local_data': [{'p': '(w+1)', 'cp': 2, 'kod': 8, 'red': -1, 'normp': 2, 'rootno': 1, 'ord_cond': 1, 'ord_disc': 4, 'ord_den_j': 4}, {'p': '(w^3-5*w+1)', 'cp': 2, 'kod': 6, 'red': -1, 'normp': 11, 'rootno': 1, 'ord_cond': 1, 'ord_disc': 2, 'ord_den_j': 2}], 'minD': '(w^3-2*w^2-7*w+8)', 'n_bad_primes': 2, 'ngens': 0, 'non_min_p': [], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'normdisc': -1936, 'number': 4, 'omega': {'__RealLiteral__': 0, 'data': '772.33024567541227973248421603009861519', 'prec': 130}, 'potential_good_reduction': False, 'q_curve': False, 'rank': 0, 'rank_bounds': [0, 0], 'reducible_primes': [2, 3], 'reg': 1, 'root_analytic_conductor': 10.851332115805096, 'semistable': True, 'sha': 1, 'short_class_label': '22.1-b', 'short_label': '22.1-b4', 'signature': [4, 0], 'tamagawa_product': 4, 'torsion_gens': ['[[1,2,-1,-1],[6,9,-1,-2],[1,0,0,0]]'], 'torsion_order': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6], 'trace_hash': 68478933159936899}
Elliptic curve data - 4.4.6809.1-22.1-b4