{"torsion_structure": [2, 2], "ainvs": "1,-2,0,1;2,-2,-1,1;-1,0,1,0;-23,-100,6,26;-75,-358,20,93", "cm": 0, "torsion_gens": ["[[-1,-5,0,1],[0,-2,1,1],[1,0,0,0]]", "[[-4,-7/4,1/4,1/4],[17/8,-35/8,1/4,2],[1,0,0,0]]"], "number": 3, "rank": 0, "field_label": "4.4.1125.1", "galois_images": ["2Cs"], "conductor_norm": 31, "abs_disc": 1125, "iso_nlabel": 1, "rank_bounds": [0, 0], "conductor_ideal": "(-w^3+5*w-2)", "base_change": [], "local_data": [{"p": "(-w^3+5*w-2)", "cp": 2, "kod": 12, "red": -1, "normp": 31, "rootno": 1, "ord_cond": 1, "ord_disc": 8, "ord_den_j": 8}], "analytic_rank": 0, "minD": "(-1018*w^3+81*w^2+3251*w-417)", "label": "4.4.1125.1-31.2-b3", "jinv": "71907211552629246852068/852891037441,341360629620385537992211/852891037441,-32551084210297485030913/852891037441,-96230619458397643875589/852891037441", "conductor_label": "31.2", "class_deg": 8, "reg": 1, "class_size": 6, "class_label": "4.4.1125.1-31.2-b", "iso_label": "b", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "31.2-b3", "short_class_label": "31.2-b", "isogeny_matrix": [[1, 8, 2, 4, 4, 8], [8, 1, 4, 8, 2, 4], [2, 4, 1, 2, 2, 4], [4, 8, 2, 1, 4, 8], [4, 2, 2, 4, 1, 2], [8, 4, 4, 8, 2, 1]], "torsion_order": 4, "equation": "{y}^2+\\left(a^{3}-2a+1\\right){x}{y}+\\left(a^{2}-1\\right){y}={x}^{3}+\\left(a^{3}-a^{2}-2a+2\\right){x}^{2}+\\left(26a^{3}+6a^{2}-100a-23\\right){x}+93a^{3}+20a^{2}-358a-75", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 1168144009904954139, "heights": [], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "47.350849016237351079574241255528789454", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(-w^3+5*w-2)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.705864781284238", "prec": 57}, "sha": 4, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2], "semistable": true, "disc": "(58*w^3-278*w^2-255*w+1713)", "normdisc": 852891037441, "conductor_norm_factors": [31], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 4.603996941607043, "cm_type": 0}