{"torsion_structure": [2], "ainvs": "1,0,0,0;-2,-6,-1,1;0,0,0,0;-17,-30,-5,5;-19,-36,-6,6", "cm": 0, "torsion_gens": ["[[-2,0,0,0],[1,0,0,0],[1,0,0,0]]"], "number": 4, "rank": 0, "field_label": "4.4.4205.1", "galois_images": ["2B", "5B.4.2"], "conductor_norm": 49, "abs_disc": 4205, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(-w^3+w^2+6*w)", "base_change": ["2.2.29.1-7.1-a1", "2.2.29.1-175.6-b1"], "local_data": [{"p": "(-w^3+2*w^2+3*w-3)", "cp": 1, "kod": 5, "red": -1, "normp": 7, "rootno": 1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}, {"p": "(w^2-2*w-3)", "cp": 1, "kod": 5, "red": -1, "normp": 7, "rootno": 1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}], "analytic_rank": 0, "minD": "(-w^3+w^2+6*w)", "label": "4.4.4205.1-49.2-a4", "jinv": "268859728/7,568988178/7,94831363/7,-94831363/7", "conductor_label": "49.2", "class_deg": 10, "reg": 1, "class_size": 4, "class_label": "4.4.4205.1-49.2-a", "iso_label": "a", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "49.2-a4", "short_class_label": "49.2-a", "isogeny_matrix": [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], "torsion_order": 2, "equation": "{y}^2+{x}{y}={x}^{3}+\\left(a^{3}-a^{2}-6a-2\\right){x}^{2}+\\left(5a^{3}-5a^{2}-30a-17\\right){x}+6a^{3}-6a^{2}-36a-19", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 1598418691986978931, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "411.67676832003757634179099024420667465", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 1, "bad_primes": ["(-w^3+2*w^2+3*w-3)", "(w^2-2*w-3)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.58713317020868", "prec": 54}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2, 5], "semistable": true, "disc": "(-w^3+w^2+6*w)", "normdisc": 49, "conductor_norm_factors": [7], "nonmax_primes": [2, 5], "nonmax_rad": 10, "root_analytic_conductor": 9.425319124803684, "cm_type": 0}