{"torsion_structure": [10], "ainvs": "1,0,0;-3,-1,1;0,0,0;-8,-4,4;26,7,-11", "cm": 0, "torsion_gens": ["[[1,0,0],[3,2,-2],[1,0,0]]"], "number": 3, "rank": 0, "field_label": "3.3.49.1", "galois_images": ["2B", "5B.1.1"], "conductor_norm": 41, "abs_disc": 49, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(3*w^2-w-3)", "base_change": [], "local_data": [{"p": "(3*w^2-w-3)", "cp": 2, "kod": 6, "red": 1, "normp": 41, "rootno": -1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 0, "minD": "(10*w^2-7*w-9)", "label": "3.3.49.1-41.3-a3", "jinv": "14955417009784/1681,3693705667625/1681,-6655766653200/1681", "conductor_label": "41.3", "class_deg": 10, "reg": 1, "class_size": 4, "class_label": "3.3.49.1-41.3-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "41.3-a3", "short_class_label": "41.3-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+{x}{y}={x}^{3}+\\left(a^{2}-a-3\\right){x}^{2}+\\left(4a^{2}-4a-8\\right){x}-11a^{2}+7a+26", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 651768551149539308, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "169.72842077302045463968220796267580305", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(3*w^2-w-3)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.48493834506577272754194916560764515158", "prec": 133}, "sha": 1, "torsion_primes": [2, 5], "n_bad_primes": 1, "reducible_primes": [2, 5], "semistable": true, "disc": "(10*w^2-7*w-9)", "normdisc": -1681, "conductor_norm_factors": [41], "nonmax_primes": [2, 5], "nonmax_rad": 10, "root_analytic_conductor": 1.1615392852659907, "cm_type": 0}