{"torsion_structure": [8], "ainvs": "-2,-3,1,1;-3,-3,1,1;0,0,0,0;-94,-55,20,20;402,265,-99,-92", "cm": 0, "torsion_gens": ["[[5,7,-2,-2],[-4,12,-1,-2],[1,0,0,0]]"], "number": 1, "rank": 0, "field_label": "4.4.1125.1", "galois_images": ["2B"], "conductor_norm": 31, "abs_disc": 1125, "iso_nlabel": 1, "rank_bounds": [0, 0], "conductor_ideal": "(2*w^3-8*w+1)", "base_change": [], "local_data": [{"p": "(2*w^3-8*w+1)", "cp": 2, "kod": 6, "red": -1, "normp": 31, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 0, "minD": "(w^3+w^2-3*w+4)", "label": "4.4.1125.1-31.4-b1", "jinv": "1543360584318567026/961,7326190029022112587/961,-698632890478410244/961,-2065276808971305476/961", "conductor_label": "31.4", "class_deg": 8, "reg": 1, "class_size": 6, "class_label": "4.4.1125.1-31.4-b", "iso_label": "b", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "31.4-b1", "short_class_label": "31.4-b", "isogeny_matrix": [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], "torsion_order": 8, "equation": "{y}^2+\\left(a^{3}+a^{2}-3a-2\\right){x}{y}={x}^{3}+\\left(a^{3}+a^{2}-3a-3\\right){x}^{2}+\\left(20a^{3}+20a^{2}-55a-94\\right){x}-92a^{3}-99a^{2}+265a+402", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 1168144009904954139, "heights": [], "isodeg": [1, 2, 4, 8], "omega": {"__RealLiteral__": 0, "data": "757.61358425979761727318786008846063126", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(2*w^3-8*w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.705864781284238", "prec": 57}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2], "semistable": true, "disc": "(w^3+w^2-3*w+4)", "normdisc": 961, "conductor_norm_factors": [31], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 4.603996941607043, "cm_type": 0}