{"torsion_structure": [], "ainvs": "0,1,-3,-1,1;1,-2,-1,1,0;3,8,-7,-3,2;-1,4,-2,-2,1;-5,-6,7,3,-2", "cm": 0, "torsion_gens": [], "number": 1, "rank": 1, "field_label": "5.5.36497.1", "galois_images": [], "conductor_norm": 37, "abs_disc": 36497, "iso_nlabel": 2, "rank_bounds": [1, 1], "conductor_ideal": "(w^4-2*w^3-2*w^2+4*w+1)", "base_change": [], "local_data": [{"p": "(w^4-2*w^3-2*w^2+4*w+1)", "cp": 1, "kod": 5, "red": -1, "normp": 37, "rootno": 1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}], "analytic_rank": 1, "minD": "(w^4-2*w^3-2*w^2+4*w+1)", "label": "5.5.36497.1-37.1-c1", "jinv": "-5310421/37,2658172/37,27788818/37,-600304/37,-12336731/37", "conductor_label": "37.1", "class_deg": 1, "reg": {"__RealLiteral__": 0, "data": "0.0020171567951169378037527381152384954343", "prec": 140}, "class_size": 1, "class_label": "5.5.36497.1-37.1-c", "iso_label": "c", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "37.1-c1", "short_class_label": "37.1-c", "isogeny_matrix": [[1]], "torsion_order": 1, "equation": "{y}^2+\\left(a^{4}-a^{3}-3a^{2}+a\\right){x}{y}+\\left(2a^{4}-3a^{3}-7a^{2}+8a+3\\right){y}={x}^{3}+\\left(a^{3}-a^{2}-2a+1\\right){x}^{2}+\\left(a^{4}-2a^{3}-2a^{2}+4a-1\\right){x}-2a^{4}+3a^{3}+7a^{2}-6a-5", "gens": ["[[0,0,0,0,0],[-1,-5,3,2,-1],[1,0,0,0,0]]"], "ngens": 1, "signature": [5, 0], "trace_hash": 1159004206983527596, "heights": [{"__RealLiteral__": 0, "data": "0.0020171567951169378037527381152384954343", "prec": 140}], "isodeg": [1], "omega": {"__RealLiteral__": 0, "data": "31970.227483066549679342196147256589036", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 1, "bad_primes": ["(w^4-2*w^3-2*w^2+4*w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.68782263", "prec": 34}, "sha": 1, "torsion_primes": [], "n_bad_primes": 1, "reducible_primes": [], "semistable": true, "disc": "(-w^4+2*w^3+2*w^2-4*w-1)", "normdisc": -37, "conductor_norm_factors": [37], "nonmax_primes": [], "nonmax_rad": 1, "root_analytic_conductor": 24.495556460923794, "cm_type": 0}