{"torsion_structure": [2, 2], "ainvs": "1,0;-1,1;1,1;-14295,4239;-254898,75585", "cm": 0, "torsion_gens": ["[[-341/4,25],[337/8,-13],[1,0]]", "[[-11,3],[5,-2],[1,0]]"], "number": 3, "rank": 0, "field_label": "2.2.33.1", "galois_images": ["2Cs"], "conductor_norm": 33, "abs_disc": 33, "iso_nlabel": 1, "rank_bounds": [0, 0], "conductor_ideal": "(-2*w+1)", "base_change": ["363.b2", "99.b2"], "local_data": [{"p": "(-2*w+7)", "cp": 2, "kod": 16, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 12, "ord_den_j": 12}, {"p": "(-4*w-9)", "cp": 2, "kod": 8, "red": -1, "normp": 11, "rootno": 1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}], "analytic_rank": 0, "minD": "(88209)", "label": "2.2.33.1-33.1-b3", "jinv": "169112377/88209,0", "conductor_label": "33.1", "class_deg": 8, "reg": 1, "class_size": 6, "class_label": "2.2.33.1-33.1-b", "iso_label": "b", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "33.1-b3", "short_class_label": "33.1-b", "isogeny_matrix": [[1, 8, 4, 2, 8, 4], [8, 1, 2, 4, 4, 8], [4, 2, 1, 2, 2, 4], [2, 4, 2, 1, 4, 2], [8, 4, 2, 4, 1, 8], [4, 8, 4, 2, 8, 1]], "torsion_order": 4, "equation": "{y}^2+{x}{y}+\\left(a+1\\right){y}={x}^{3}+\\left(a-1\\right){x}^{2}+\\left(4239a-14295\\right){x}+75585a-254898", "gens": [], "ngens": 0, "signature": [2, 0], "trace_hash": 1991450565965604187, "heights": [], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "7.5330122669145064435384716528544758739", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 4, "bad_primes": ["(-2*w+7)", "(-4*w-9)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.32783227942749872640669424935494634768", "prec": 133}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2], "semistable": true, "disc": "(88209)", "normdisc": 7780827681, "conductor_norm_factors": [3, 11], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 1.2303367836963277, "cm_type": 0}