{"torsion_structure": [4], "ainvs": "-2,0,1,0,0;0,5,-3,-2,1;1,6,-3,-2,1;3,5,-4,-2,1;1,0,-15,-3,4", "cm": 0, "torsion_gens": ["[[-1,-2,7,2,-2],[2,-5,-12,-1,3],[1,0,0,0,0]]"], "number": 3, "rank": 0, "field_label": "5.5.36497.1", "galois_images": ["2B", "7B.6.1"], "conductor_norm": 39, "abs_disc": 36497, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(-2*w^4+3*w^3+7*w^2-6*w-2)", "base_change": [], "local_data": [{"p": "(w^2-1)", "cp": 1, "kod": 11, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 7, "ord_den_j": 7}, {"p": "(w^3-3*w)", "cp": 1, "kod": 5, "red": 1, "normp": 13, "rootno": -1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}], "analytic_rank": 0, "minD": "(2*w^4-3*w^3-6*w^2+8*w-9)", "label": "5.5.36497.1-39.1-a3", "jinv": "11953519/28431,-51097538/28431,4095677/9477,5295800/9477,-1065196/28431", "conductor_label": "39.1", "class_deg": 28, "reg": 1, "class_size": 8, "class_label": "5.5.36497.1-39.1-a", "iso_label": "a", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "39.1-a3", "short_class_label": "39.1-a", "isogeny_matrix": [[1, 28, 7, 14, 28, 2, 4, 4], [28, 1, 4, 2, 4, 14, 7, 28], [7, 4, 1, 2, 4, 14, 28, 28], [14, 2, 2, 1, 2, 7, 14, 14], [28, 4, 4, 2, 1, 14, 28, 7], [2, 14, 14, 7, 14, 1, 2, 2], [4, 7, 28, 14, 28, 2, 1, 4], [4, 28, 28, 14, 7, 2, 4, 1]], "torsion_order": 4, "equation": "{y}^2+\\left(a^{2}-2\\right){x}{y}+\\left(a^{4}-2a^{3}-3a^{2}+6a+1\\right){y}={x}^{3}+\\left(a^{4}-2a^{3}-3a^{2}+5a\\right){x}^{2}+\\left(a^{4}-2a^{3}-4a^{2}+5a+3\\right){x}+4a^{4}-3a^{3}-15a^{2}+1", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 412151449541545432, "heights": [], "isodeg": [1, 2, 4, 7, 14, 28], "omega": {"__RealLiteral__": 0, "data": "2915.1531533189314451713334428301496546", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 1, "bad_primes": ["(w^2-1)", "(w^3-3*w)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.953702256", "prec": 37}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2, 7], "semistable": true, "disc": "(-7*w^4+10*w^3+21*w^2-19*w-5)", "normdisc": -28431, "conductor_norm_factors": [3, 13], "nonmax_primes": [2, 7], "nonmax_rad": 14, "root_analytic_conductor": 24.624850242282925, "cm_type": 0}