{"torsion_structure": [], "ainvs": "0,-2,1/3,1/3;5,0,-1,0;0,1,0,0;9,-1,-1,0;5,-2,-2/3,1/3", "cm": 0, "torsion_gens": [], "number": 2, "rank": 0, "field_label": "4.4.19821.1", "galois_images": ["3B"], "conductor_norm": 27, "abs_disc": 19821, "iso_nlabel": 3, "rank_bounds": [0, 0], "conductor_ideal": "(1/3*w^3-2/3*w^2-2*w+1)", "base_change": [], "local_data": [{"p": "(-1/3*w^3-1/3*w^2+3*w+2)", "cp": 1, "kod": -4, "red": 0, "normp": 3, "rootno": 1, "ord_cond": 3, "ord_disc": 9, "ord_den_j": 0}], "analytic_rank": 0, "minD": "(-16/3*w^3+17/3*w^2+38*w-31)", "label": "4.4.19821.1-27.2-d2", "jinv": "-15892,-48583,1769/3,18512/3", "conductor_label": "27.2", "class_deg": 3, "reg": 1, "class_size": 2, "class_label": "4.4.19821.1-27.2-d", "iso_label": "d", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "27.2-d2", "short_class_label": "27.2-d", "isogeny_matrix": [[1, 3], [3, 1]], "torsion_order": 1, "equation": "{y}^2+\\left(\\frac{1}{3}a^{3}+\\frac{1}{3}a^{2}-2a\\right){x}{y}+a{y}={x}^{3}+\\left(-a^{2}+5\\right){x}^{2}+\\left(-a^{2}-a+9\\right){x}+\\frac{1}{3}a^{3}-\\frac{2}{3}a^{2}-2a+5", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 1134562545514323818, "heights": [], "isodeg": [1, 3], "omega": {"__RealLiteral__": 0, "data": "196.18602489646321997726833524973897029", "prec": 130}, "potential_good_reduction": true, "tamagawa_product": 1, "bad_primes": ["(-1/3*w^3-1/3*w^2+3*w+2)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.39349458966226", "prec": 54}, "sha": 1, "torsion_primes": [], "n_bad_primes": 1, "reducible_primes": [3], "semistable": false, "disc": "(3*w^3-2*w^2-27*w+3)", "normdisc": 19683, "conductor_norm_factors": [3], "nonmax_primes": [3], "nonmax_rad": 3, "root_analytic_conductor": 18.9942349091379, "cm_type": 0}