{"torsion_structure": [2], "ainvs": "1,0,0;7,2,-1;-5,-1,1;-50925,-91888,-27931;-5077108371,-9158882355,-2783901290", "cm": 0, "torsion_gens": ["[[1259/4,1143/2,697/4],[-1239/8,-1141/4,-701/8],[1,0,0]]"], "number": 4, "rank": 0, "field_label": "3.3.1944.1", "galois_images": ["2B"], "conductor_norm": 12, "abs_disc": 1944, "iso_nlabel": 2, "rank_bounds": [0, 0], "conductor_ideal": "(-w^2-w)", "base_change": [], "local_data": [{"p": "(-3*w^2+2*w+26)", "cp": 1, "kod": 5, "red": 1, "normp": 2, "rootno": -1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}, {"p": "(-w-1)", "cp": 2, "kod": 16, "red": -1, "normp": 2, "rootno": 1, "ord_cond": 1, "ord_disc": 12, "ord_den_j": 12}, {"p": "(-2*w^2+2*w+15)", "cp": 2, "kod": 6, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 0, "minD": "(-10*w^2+12*w+114)", "label": "3.3.1944.1-12.1-c4", "jinv": "14933/4,16577/96,-76301/192", "conductor_label": "12.1", "class_deg": 4, "reg": 1, "class_size": 4, "class_label": "3.3.1944.1-12.1-c", "iso_label": "c", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "12.1-c4", "short_class_label": "12.1-c", "isogeny_matrix": [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], "torsion_order": 2, "equation": "{y}^2+{x}{y}+\\left(a^{2}-a-5\\right){y}={x}^{3}+\\left(-a^{2}+2a+7\\right){x}^{2}+\\left(-27931a^{2}-91888a-50925\\right){x}-2783901290a^{2}-9158882355a-5077108371", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 1634953353708589734, "heights": [], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "59.602000201591285190032371562677522735", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 4, "bad_primes": ["(-3*w^2+2*w+26)", "(-w-1)", "(-2*w^2+2*w+15)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.3518008161403589473723816625889584465", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 3, "reducible_primes": [2], "semistable": true, "disc": "(10*w^2-12*w-114)", "normdisc": 73728, "conductor_norm_factors": [2, 3], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 5.9614269257714705, "cm_type": 0}