{"torsion_structure": [], "ainvs": "1,1,0,0,0;0,6,-3,-2,1;3,2,-4,-1,1;-4,-16,1,3,0;-4,-16,-22,1,5", "cm": 0, "torsion_gens": [], "number": 1, "rank": 0, "field_label": "5.5.65657.1", "galois_images": [], "conductor_norm": 27, "abs_disc": 65657, "iso_nlabel": 1, "rank_bounds": [0, 0], "conductor_ideal": "(2*w^4-3*w^3-9*w^2+9*w+7)", "base_change": [], "local_data": [{"p": "(-w^4+w^3+4*w^2-2*w-2)", "cp": 1, "kod": 4, "red": 0, "normp": 3, "rootno": -1, "ord_cond": 3, "ord_disc": 5, "ord_den_j": 0}], "analytic_rank": 0, "minD": "(-w^4+2*w^3+5*w^2-5*w-7)", "label": "5.5.65657.1-27.1-b1", "jinv": "-13950,-180889,-523999,-33919,124002", "conductor_label": "27.1", "class_deg": 1, "reg": 1, "class_size": 1, "class_label": "5.5.65657.1-27.1-b", "iso_label": "b", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "27.1-b1", "short_class_label": "27.1-b", "isogeny_matrix": [[1]], "torsion_order": 1, "equation": "{y}^2+\\left(a+1\\right){x}{y}+\\left(a^{4}-a^{3}-4a^{2}+2a+3\\right){y}={x}^{3}+\\left(a^{4}-2a^{3}-3a^{2}+6a\\right){x}^{2}+\\left(3a^{3}+a^{2}-16a-4\\right){x}+5a^{4}+a^{3}-22a^{2}-16a-4", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 699577139858157778, "heights": [], "isodeg": [1], "omega": {"__RealLiteral__": 0, "data": "410.85828418403568039134610162517079673", "prec": 130}, "potential_good_reduction": true, "tamagawa_product": 1, "bad_primes": ["(-w^4+w^3+4*w^2-2*w-2)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.60343563", "prec": 34}, "sha": 1, "torsion_primes": [], "n_bad_primes": 1, "reducible_primes": [], "semistable": false, "disc": "(w^4-2*w^3-5*w^2+5*w+7)", "normdisc": -243, "conductor_norm_factors": [3], "nonmax_primes": [], "nonmax_rad": 1, "root_analytic_conductor": 31.83577652457452, "cm_type": 0}