{"torsion_structure": [], "ainvs": "-6,-8,9,3,-2;2,7,-4,-2,1;1,1,0,0,0;6,-3,-21,-3,5;-4,-33,-40,2,9", "cm": 0, "torsion_gens": [], "number": 2, "rank": 1, "field_label": "5.5.65657.1", "galois_images": ["3B"], "conductor_norm": 43, "abs_disc": 65657, "iso_nlabel": 0, "rank_bounds": [1, 1], "conductor_ideal": "(w^4-2*w^3-4*w^2+4*w+2)", "base_change": [], "local_data": [{"p": "(w^4-2*w^3-4*w^2+4*w+2)", "cp": 1, "kod": 7, "red": -1, "normp": 43, "rootno": 1, "ord_cond": 1, "ord_disc": 3, "ord_den_j": 3}], "analytic_rank": 1, "minD": "(-4*w^4+5*w^3+18*w^2-13*w-23)", "label": "5.5.65657.1-43.1-a2", "jinv": "10232774495362/79507,55492835852009/79507,43993086493009/79507,-32340604970044/79507,-23968185390845/79507", "conductor_label": "43.1", "class_deg": 3, "reg": {"__RealLiteral__": 0, "data": "0.23469217616037164956641812831120486941", "prec": 133}, "class_size": 2, "class_label": "5.5.65657.1-43.1-a", "iso_label": "a", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "43.1-a2", "short_class_label": "43.1-a", "isogeny_matrix": [[1, 3], [3, 1]], "torsion_order": 1, "equation": "{y}^2+\\left(-2a^{4}+3a^{3}+9a^{2}-8a-6\\right){x}{y}+\\left(a+1\\right){y}={x}^{3}+\\left(a^{4}-2a^{3}-4a^{2}+7a+2\\right){x}^{2}+\\left(5a^{4}-3a^{3}-21a^{2}-3a+6\\right){x}+9a^{4}+2a^{3}-40a^{2}-33a-4", "gens": ["[[-2,0,9,1,-2],[0,16,11,-3,-2],[1,0,0,0,0]]"], "ngens": 1, "signature": [5, 0], "trace_hash": 838346031727313046, "heights": [{"__RealLiteral__": 0, "data": "0.23469217616037164956641812831120486941", "prec": 133}], "isodeg": [1, 3], "omega": {"__RealLiteral__": 0, "data": "624.77761162954924657105646691686018884", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 1, "bad_primes": ["(w^4-2*w^3-4*w^2+4*w+2)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.86123519", "prec": 34}, "sha": 1, "torsion_primes": [], "n_bad_primes": 1, "reducible_primes": [3], "semistable": true, "disc": "(-4*w^4+5*w^3+18*w^2-13*w-23)", "normdisc": -79507, "conductor_norm_factors": [43], "nonmax_primes": [3], "nonmax_rad": 3, "root_analytic_conductor": 33.352309832413596, "cm_type": 0}