{"torsion_structure": [10], "ainvs": "1,0,0;0,-1,0;1,1,0;-1,0,0;0,-1,0", "cm": 0, "torsion_gens": ["[[0,0,0],[0,-1,0],[1,0,0]]"], "number": 4, "rank": 0, "field_label": "3.3.49.1", "galois_images": ["2B", "5B.1.1"], "conductor_norm": 71, "abs_disc": 49, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(4*w^2-3*w-5)", "base_change": [], "local_data": [{"p": "(4*w^2-3*w-5)", "cp": 1, "kod": 5, "red": 1, "normp": 71, "rootno": -1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}], "analytic_rank": 0, "minD": "(4*w^2-3*w-5)", "label": "3.3.49.1-71.1-a4", "jinv": "1959524/71,710952/71,-713073/71", "conductor_label": "71.1", "class_deg": 10, "reg": 1, "class_size": 4, "class_label": "3.3.49.1-71.1-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "71.1-a4", "short_class_label": "71.1-a", "isogeny_matrix": [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], "torsion_order": 10, "equation": "{y}^2+{x}{y}+\\left(a+1\\right){y}={x}^{3}-a{x}^{2}-{x}-a", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 1967013989759310318, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "411.20090971333349774675156964195137588", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 1, "bad_primes": ["(4*w^2-3*w-5)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.58742987101904785392393081377421625126", "prec": 133}, "sha": 1, "torsion_primes": [2, 5], "n_bad_primes": 1, "reducible_primes": [2, 5], "semistable": true, "disc": "(w+4)", "normdisc": -71, "conductor_norm_factors": [71], "nonmax_primes": [2, 5], "nonmax_rad": 10, "root_analytic_conductor": 1.2728571065687284, "cm_type": 0}