{"torsion_structure": [2, 2], "ainvs": "0,1;-1,0;0,1;-69,-41;301,191", "cm": 0, "torsion_gens": ["[[-5,-4],[8,4],[1,0]]", "[[1,2],[-4,-2],[1,0]]"], "number": 5, "rank": 1, "field_label": "2.2.17.1", "galois_images": ["2Cs"], "conductor_norm": 576, "abs_disc": 17, "iso_nlabel": 13, "rank_bounds": [1, 1], "conductor_ideal": "(15*w+12)", "base_change": [], "local_data": [{"p": "(-w+2)", "cp": 4, "kod": -12, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 6, "ord_disc": 18, "ord_den_j": 0}, {"p": "(3)", "cp": 2, "kod": 6, "red": -1, "normp": 9, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 1, "minD": "(297*w+4500)", "label": "2.2.17.1-576.7-n5", "jinv": "36913625/9,-14326000/9", "conductor_label": "576.7", "class_deg": 16, "reg": {"__RealLiteral__": 0, "data": "0.41957905563550343252480463254077013701", "prec": 133}, "class_size": 8, "class_label": "2.2.17.1-576.7-n", "iso_label": "n", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "576.7-n5", "short_class_label": "576.7-n", "isogeny_matrix": [[1, 16, 8, 4, 8, 2, 16, 4], [16, 1, 8, 4, 2, 8, 4, 16], [8, 8, 1, 2, 4, 4, 8, 8], [4, 4, 2, 1, 2, 2, 4, 4], [8, 2, 4, 2, 1, 4, 2, 8], [2, 8, 4, 2, 4, 1, 8, 2], [16, 4, 8, 4, 2, 8, 1, 16], [4, 16, 8, 4, 8, 2, 16, 1]], "torsion_order": 4, "equation": "{y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\\left(-41a-69\\right){x}+191a+301", "gens": ["[[-3,-3],[20,12],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 406536863569814210, "heights": [{"__RealLiteral__": 0, "data": "0.41957905563550343252480463254077013701", "prec": 133}], "isodeg": [1, 2, 4, 8], "omega": {"__RealLiteral__": 0, "data": "18.097976228155525669241568394557159656", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 8, "bad_primes": ["(-w+2)", "(3)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.8417019752157669289529360629512751675", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2], "semistable": false, "disc": "(297*w+4500)", "normdisc": 21233664, "conductor_norm_factors": [2, 3], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 1.8049643770635033, "cm_type": 0}