{"torsion_structure": [2], "ainvs": "1,0,0;-2,0,1;-1,0,1;81,-190,-221;1532,-2384,-2926", "cm": 0, "torsion_gens": ["[[47/4,-4,-7],[-43/8,2,3],[1,0,0]]"], "number": 4, "rank": 0, "field_label": "3.3.49.1", "galois_images": ["2B", "5B.1.2"], "conductor_norm": 71, "abs_disc": 49, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(w^2-6)", "base_change": [], "local_data": [{"p": "(w^2-6)", "cp": 10, "kod": 14, "red": 1, "normp": 71, "rootno": -1, "ord_cond": 1, "ord_disc": 10, "ord_den_j": 10}], "analytic_rank": 0, "minD": "(-1063665*w^2-281489*w+2300913)", "label": "3.3.49.1-71.3-a4", "jinv": "-697032567862883246911701/3255243551009881201,808193592087701284035551/3255243551009881201,1128735985778740212430417/3255243551009881201", "conductor_label": "71.3", "class_deg": 10, "reg": 1, "class_size": 4, "class_label": "3.3.49.1-71.3-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "71.3-a4", "short_class_label": "71.3-a", "isogeny_matrix": [[1, 5, 10, 2], [5, 1, 2, 10], [10, 2, 1, 5], [2, 10, 5, 1]], "torsion_order": 2, "equation": "{y}^2+{x}{y}+\\left(a^{2}-1\\right){y}={x}^{3}+\\left(a^{2}-2\\right){x}^{2}+\\left(-221a^{2}-190a+81\\right){x}-2926a^{2}-2384a+1532", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 1967013989759310318, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "1.6448036388533339909870062785678055035", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 10, "bad_primes": ["(w^2-6)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.58742987101904785392393081377421625126", "prec": 133}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2, 5], "semistable": true, "disc": "(1063665*w^2+281489*w-2300913)", "normdisc": -3255243551009881201, "conductor_norm_factors": [71], "nonmax_primes": [2, 5], "nonmax_rad": 10, "root_analytic_conductor": 1.2728571065687284, "cm_type": 0}