{"torsion_structure": [4], "ainvs": "1,1,0;-2,1,1;0,0,0;4,4,1;0,0,0", "cm": 0, "torsion_gens": ["[[2,1,0],[-8,1,3],[1,0,0]]"], "number": 3, "rank": 0, "field_label": "3.3.316.1", "galois_images": ["2B"], "conductor_norm": 16, "abs_disc": 316, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(w^2-w-6)", "base_change": [], "local_data": [{"p": "(w)", "cp": 4, "kod": 8, "red": 1, "normp": 2, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}, {"p": "(-w+1)", "cp": 2, "kod": -3, "red": 0, "normp": 2, "rootno": 1, "ord_cond": 3, "ord_disc": 10, "ord_den_j": 0}], "analytic_rank": 0, "minD": "(-4*w^2-16*w+20)", "label": "3.3.316.1-16.4-a3", "jinv": "7961/4,-775/2,-3655/4", "conductor_label": "16.4", "class_deg": 4, "reg": 1, "class_size": 4, "class_label": "3.3.316.1-16.4-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "16.4-a3", "short_class_label": "16.4-a", "isogeny_matrix": [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], "torsion_order": 4, "equation": "{y}^2+\\left(a+1\\right){x}{y}={x}^{3}+\\left(a^{2}+a-2\\right){x}^{2}+\\left(a^{2}+4a+4\\right){x}", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 1787507441970155950, "heights": [], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "58.083152015845881063812216877556237956", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 8, "bad_primes": ["(w)", "(-w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.6337162895168799074626233256424132113", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2], "semistable": false, "disc": "(4*w^2+16*w-20)", "normdisc": -16384, "conductor_norm_factors": [2], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 2.5215568184096373, "cm_type": 0}