{"torsion_structure": [2, 4], "ainvs": "1,0;-1,0;1,0;-21,0;41,0", "cm": 0, "torsion_gens": ["[[11/4,0],[-15/8,0],[1,0]]", "[[3,-1],[-6,1],[1,0]]"], "number": 4, "rank": 1, "field_label": "2.2.8.1", "galois_images": ["2Cs"], "conductor_norm": 1922, "abs_disc": 8, "iso_nlabel": 2, "rank_bounds": [1, 1], "conductor_ideal": "(31*w)", "base_change": ["62.a3", "1984.f3"], "local_data": [{"p": "(w)", "cp": 4, "kod": 8, "red": 1, "normp": 2, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}, {"p": "(-4*w-1)", "cp": 2, "kod": 6, "red": -1, "normp": 31, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}, {"p": "(4*w-1)", "cp": 2, "kod": 6, "red": -1, "normp": 31, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 1, "minD": "(3844)", "label": "2.2.8.1-1922.1-c4", "jinv": "979146657/3844,0", "conductor_label": "1922.1", "class_deg": 8, "reg": {"__RealLiteral__": 0, "data": "1.0184184579991417065135578396631523777", "prec": 130}, "class_size": 6, "class_label": "2.2.8.1-1922.1-c", "iso_label": "c", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "1922.1-c4", "short_class_label": "1922.1-c", "isogeny_matrix": [[1, 8, 4, 2, 8, 4], [8, 1, 2, 4, 4, 8], [4, 2, 1, 2, 2, 4], [2, 4, 2, 1, 4, 2], [8, 4, 2, 4, 1, 8], [4, 8, 4, 2, 8, 1]], "torsion_order": 8, "equation": "{y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-21{x}+41", "gens": ["[[5,-1],[4,-3],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 1660126346961383010, "heights": [{"__RealLiteral__": 0, "data": "1.0184184579991417065135578396631523777", "prec": 130}], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "19.668893631030871739287294565309386895", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 16, "bad_primes": ["(w)", "(-4*w-1)", "(4*w-1)"], "Lvalue": {"__RealLiteral__": 0, "data": "3.5410430318336561767373780957863814700", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 3, "reducible_primes": [2], "semistable": true, "disc": "(3844)", "normdisc": 14776336, "conductor_norm_factors": [2, 31], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 1.6734852653029488, "cm_type": 0}