{"torsion_structure": [10], "ainvs": "1,-2,0,1,0;2,0,-4,0,1;-1,-3,1,1,0;0,6,-3,-2,1;0,-2,0,1,0", "cm": 0, "torsion_gens": ["[[0,3,0,-1,0],[3,-2,-1,1,0],[1,0,0,0,0]]"], "number": 4, "rank": 0, "field_label": "5.5.14641.1", "galois_images": ["2B", "5B.1.1"], "conductor_norm": 23, "abs_disc": 14641, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(-w^4+2*w^2+1)", "base_change": [], "local_data": [{"p": "(-w^4+2*w^2+1)", "cp": 5, "kod": 9, "red": 1, "normp": 23, "rootno": -1, "ord_cond": 1, "ord_disc": 5, "ord_den_j": 5}], "analytic_rank": 0, "minD": "(-8*w^4+17*w^3+15*w^2-45*w-3)", "label": "5.5.14641.1-23.4-a4", "jinv": "12180979828/6436343,-48623181064/6436343,23073195843/6436343,785056248/6436343,-703293464/6436343", "conductor_label": "23.4", "class_deg": 10, "reg": 1, "class_size": 4, "class_label": "5.5.14641.1-23.4-a", "iso_label": "a", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "23.4-a4", "short_class_label": "23.4-a", "isogeny_matrix": [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], "torsion_order": 10, "equation": "{y}^2+\\left(a^{3}-2a+1\\right){x}{y}+\\left(a^{3}+a^{2}-3a-1\\right){y}={x}^{3}+\\left(a^{4}-4a^{2}+2\\right){x}^{2}+\\left(a^{4}-2a^{3}-3a^{2}+6a\\right){x}+a^{3}-2a", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 1894256519342967484, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "1986.2521339973071898146350140826083125", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 5, "bad_primes": ["(-w^4+2*w^2+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.820765345", "prec": 37}, "sha": 1, "torsion_primes": [2, 5], "n_bad_primes": 1, "reducible_primes": [2, 5], "semistable": true, "disc": "(-8*w^4+17*w^3+15*w^2-45*w-3)", "normdisc": -6436343, "conductor_norm_factors": [23], "nonmax_primes": [2, 5], "nonmax_rad": 10, "root_analytic_conductor": 14.794377883723698, "cm_type": 0}