{"torsion_structure": [4], "ainvs": "0,1,0;3,1,-1;0,1,0;10275,1279,-2419;18000022,2242268,-4236156", "cm": 0, "torsion_gens": ["[[192,24,-45],[-5252,-655,1236],[1,0,0]]"], "number": 8, "rank": 0, "field_label": "3.3.316.1", "galois_images": ["2B"], "conductor_norm": 8, "abs_disc": 316, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(-w^2+2)", "base_change": [], "local_data": [{"p": "(w)", "cp": 1, "kod": -2, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 3, "ord_disc": 11, "ord_den_j": 0}], "analytic_rank": 0, "minD": "(-7*w^2+10*w+10)", "label": "3.3.316.1-8.2-a8", "jinv": "113696309796,-290083733531,103101005876", "conductor_label": "8.2", "class_deg": 16, "reg": 1, "class_size": 8, "class_label": "3.3.316.1-8.2-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "8.2-a8", "short_class_label": "8.2-a", "isogeny_matrix": [[1, 8, 16, 8, 16, 4, 2, 4], [8, 1, 8, 4, 8, 2, 4, 8], [16, 8, 1, 2, 4, 4, 8, 16], [8, 4, 2, 1, 2, 2, 4, 8], [16, 8, 4, 2, 1, 4, 8, 16], [4, 2, 4, 2, 4, 1, 2, 4], [2, 4, 8, 4, 8, 2, 1, 2], [4, 8, 16, 8, 16, 4, 2, 1]], "torsion_order": 4, "equation": "{y}^2+a{x}{y}+a{y}={x}^{3}+\\left(-a^{2}+a+3\\right){x}^{2}+\\left(-2419a^{2}+1279a+10275\\right){x}-4236156a^{2}+2242268a+18000022", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 2108746725323941569, "heights": [], "isodeg": [1, 2, 4, 8, 16], "omega": {"__RealLiteral__": 0, "data": "172.69371247537083552169884823782561999", "prec": 130}, "potential_good_reduction": true, "tamagawa_product": 1, "bad_primes": ["(w)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.60717377022511650333335178914948777014", "prec": 133}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2], "semistable": false, "disc": "(7*w^2-10*w-10)", "normdisc": -2048, "conductor_norm_factors": [2], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 2.246451737239178, "cm_type": 0}