{"torsion_structure": [2], "ainvs": "0,1;0,1;0,1;-11,5;161,-50", "cm": 0, "torsion_gens": ["[[-9/2,1],[-5,7/4],[1,0]]"], "number": 4, "rank": 1, "field_label": "2.2.40.1", "galois_images": ["2B"], "conductor_norm": 12, "abs_disc": 40, "iso_nlabel": 1, "rank_bounds": [1, 1], "conductor_ideal": "(6,2*w+4)", "base_change": [], "local_data": [{"p": "(2,w)", "cp": 3, "kod": -4, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 2, "ord_disc": 8, "ord_den_j": 0}, {"p": "(3,w+2)", "cp": 2, "kod": 12, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 8, "ord_den_j": 8}], "analytic_rank": 1, "minD": "(464*w+688)", "label": "2.2.40.1-12.2-b4", "jinv": "6190492076/6561,1957662404/6561", "conductor_label": "12.2", "class_deg": 4, "reg": {"__RealLiteral__": 0, "data": "0.13132083773923640303639471058823532910", "prec": 133}, "class_size": 4, "class_label": "2.2.40.1-12.2-b", "iso_label": "b", "degree": 2, "non_min_p": [], "q_curve": false, "short_label": "12.2-b4", "short_class_label": "12.2-b", "isogeny_matrix": [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], "torsion_order": 2, "equation": "{y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\\left(5a-11\\right){x}-50a+161", "gens": ["[[5,-2],[-9,3],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 512337275404385061, "heights": [{"__RealLiteral__": 0, "data": "0.13132083773923640303639471058823532910", "prec": 133}], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "19.197852893674641673731974833763821181", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 6, "bad_primes": ["(2,w)", "(3,w+2)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.1958523550353290872652274238966359998", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2], "semistable": false, "disc": "(464*w+688)", "normdisc": -1679616, "conductor_norm_factors": [2, 3], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 1.0518743396648031, "cm_type": 0}