{"torsion_structure": [2, 10], "ainvs": "-1,-4,0,1;-4,3,2,-1;-2,0,1,0;5,-9,-7,4;-3,1,2,-1", "cm": 0, "torsion_gens": ["[[5/2,-3/4,-2,3/4],[1/4,19/8,9/8,-1],[1,0,0,0]]", "[[2,-2,-2,1],[-1,0,0,0],[1,0,0,0]]"], "number": 3, "rank": 0, "field_label": "4.4.2777.1", "galois_images": ["2Cs", "5B.1.1"], "conductor_norm": 22, "abs_disc": 2777, "iso_nlabel": 1, "rank_bounds": [0, 0], "conductor_ideal": "(-w^3+3*w)", "base_change": [], "local_data": [{"p": "(-w)", "cp": 10, "kod": 14, "red": 1, "normp": 2, "rootno": -1, "ord_cond": 1, "ord_disc": 10, "ord_den_j": 10}, {"p": "(-w^3+2*w^2+2*w-1)", "cp": 2, "kod": 6, "red": 1, "normp": 11, "rootno": -1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 0, "minD": "(-3*w^3+9*w^2+21*w-10)", "label": "4.4.2777.1-22.1-b3", "jinv": "-153356764887/123904,-75995630703/61952,252879329025/123904,189687996477/123904", "conductor_label": "22.1", "class_deg": 20, "reg": 1, "class_size": 8, "class_label": "4.4.2777.1-22.1-b", "iso_label": "b", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "22.1-b3", "short_class_label": "22.1-b", "isogeny_matrix": [[1, 5, 10, 4, 20, 2, 20, 4], [5, 1, 2, 20, 4, 10, 4, 20], [10, 2, 1, 10, 2, 5, 2, 10], [4, 20, 10, 1, 5, 2, 20, 4], [20, 4, 2, 5, 1, 10, 4, 20], [2, 10, 5, 2, 10, 1, 10, 2], [20, 4, 2, 20, 4, 10, 1, 5], [4, 20, 10, 4, 20, 2, 5, 1]], "torsion_order": 20, "equation": "{y}^2+\\left(a^{3}-4a-1\\right){x}{y}+\\left(a^{2}-2\\right){y}={x}^{3}+\\left(-a^{3}+2a^{2}+3a-4\\right){x}^{2}+\\left(4a^{3}-7a^{2}-9a+5\\right){x}-a^{3}+2a^{2}+a-3", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 2242005807546218297, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "1697.8947969928443846920318669362486947", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 20, "bad_primes": ["(-w)", "(-w^3+2*w^2+2*w-1)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.61098999014251", "prec": 54}, "sha": 1, "torsion_primes": [2, 5], "n_bad_primes": 2, "reducible_primes": [2, 5], "semistable": true, "disc": "(18*w^3-19*w^2-56*w+12)", "normdisc": 123904, "conductor_norm_factors": [2, 11], "nonmax_primes": [2, 5], "nonmax_rad": 10, "root_analytic_conductor": 6.929937670547061, "cm_type": 0}