{"torsion_structure": [2], "ainvs": "-2,-1,1,0,0;1,-4,-1,1,0;-2,-1,1,0,0;-11,8,6,-2,-1;-75,206,-60,-88,36", "cm": 0, "torsion_gens": ["[[1,-8,4,4,-2],[1,-5,3,2,-1],[1,0,0,0,0]]"], "number": 3, "rank": 0, "field_label": "5.5.36497.1", "galois_images": ["2B", "3B"], "conductor_norm": 9, "abs_disc": 36497, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(w^2-w-2)", "base_change": [], "local_data": [{"p": "(w^2-1)", "cp": 2, "kod": -16, "red": 0, "normp": 3, "rootno": -1, "ord_cond": 2, "ord_disc": 18, "ord_den_j": 12}], "analytic_rank": 0, "minD": "(12*w^4-25*w^3-19*w^2+92*w-4)", "label": "5.5.36497.1-9.1-a3", "jinv": "1654749596218451752/531441,2377533227165763589/531441,-826730295123875959/177147,-359821343885971159/177147,679068463130598740/531441", "conductor_label": "9.1", "class_deg": 6, "reg": 1, "class_size": 4, "class_label": "5.5.36497.1-9.1-a", "iso_label": "a", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "9.1-a3", "short_class_label": "9.1-a", "isogeny_matrix": [[1, 6, 3, 2], [6, 1, 2, 3], [3, 2, 1, 6], [2, 3, 6, 1]], "torsion_order": 2, "equation": "{y}^2+\\left(a^{2}-a-2\\right){x}{y}+\\left(a^{2}-a-2\\right){y}={x}^{3}+\\left(a^{3}-a^{2}-4a+1\\right){x}^{2}+\\left(-a^{4}-2a^{3}+6a^{2}+8a-11\\right){x}+36a^{4}-88a^{3}-60a^{2}+206a-75", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 228563232576017716, "heights": [], "isodeg": [1, 2, 3, 6], "omega": {"__RealLiteral__": 0, "data": "386.56097996220412970699858192690032178", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(w^2-1)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.01171790", "prec": 34}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2, 3], "semistable": false, "disc": "(-4*w^4+20*w^3-13*w^2-39*w+88)", "normdisc": 387420489, "conductor_norm_factors": [3], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 21.2662731720259, "cm_type": 0}