{"torsion_structure": [2], "ainvs": "-4,-1,1,0;-3,-4,0,1;-4,-1,1,0;-2,-4,0,1;-1,7,1,-2", "cm": 0, "torsion_gens": ["[[1,0,0,0],[4,1,-1,0],[1,0,0,0]]"], "number": 1, "rank": 1, "field_label": "4.4.5125.1", "galois_images": ["2B"], "conductor_norm": 55, "abs_disc": 5125, "iso_nlabel": 1, "rank_bounds": [1, 1], "conductor_ideal": "(w^3-4*w)", "base_change": [], "local_data": [{"p": "(-w^3+w^2+4*w+1)", "cp": 2, "kod": 8, "red": -1, "normp": 5, "rootno": 1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}, {"p": "(-w)", "cp": 4, "kod": 8, "red": 1, "normp": 11, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}], "analytic_rank": 1, "minD": "(10*w^2+20*w-55)", "label": "4.4.5125.1-55.1-b1", "jinv": "38257458108/73205,1922722402/73205,-21993206812/73205,5932926689/73205", "conductor_label": "55.1", "class_deg": 2, "reg": {"__RealLiteral__": 0, "data": "0.76868573402422179376606928454983272516", "prec": 133}, "class_size": 2, "class_label": "4.4.5125.1-55.1-b", "iso_label": "b", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "55.1-b1", "short_class_label": "55.1-b", "isogeny_matrix": [[1, 2], [2, 1]], "torsion_order": 2, "equation": "{y}^2+\\left(a^{2}-a-4\\right){x}{y}+\\left(a^{2}-a-4\\right){y}={x}^{3}+\\left(a^{3}-4a-3\\right){x}^{2}+\\left(a^{3}-4a-2\\right){x}-2a^{3}+a^{2}+7a-1", "gens": ["[[12,3,-2,0],[-18,-2,3,-1],[1,0,0,0]]"], "ngens": 1, "signature": [4, 0], "trace_hash": 223360087217104253, "heights": [{"__RealLiteral__": 0, "data": "0.76868573402422179376606928454983272516", "prec": 133}], "isodeg": [1, 2], "omega": {"__RealLiteral__": 0, "data": "30.874097820850083723221024196263941252", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 8, "bad_primes": ["(-w^3+w^2+4*w+1)", "(-w)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.65207712160918", "prec": 54}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2], "semistable": true, "disc": "(-10*w^2-20*w+55)", "normdisc": 9150625, "conductor_norm_factors": [5, 11], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 10.556764284235115, "cm_type": 0}