{"torsion_structure": [2], "ainvs": "1,0;1,0;1,1;3138,-545;3585,-27234", "cm": 0, "torsion_gens": ["[[-29/4,10],[25/8,-11/2],[1,0]]"], "number": 8, "rank": 1, "field_label": "2.0.11.1", "galois_images": ["2B", "3B"], "conductor_norm": 27225, "abs_disc": 11, "iso_nlabel": 3, "rank_bounds": [1, 1], "conductor_ideal": "(165)", "base_change": [], "local_data": [{"p": "(-w)", "cp": 2, "kod": 16, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 12, "ord_den_j": 12}, {"p": "(w-1)", "cp": 1, "kod": 5, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}, {"p": "(-w-1)", "cp": 3, "kod": 7, "red": 1, "normp": 5, "rootno": -1, "ord_cond": 1, "ord_disc": 3, "ord_den_j": 3}, {"p": "(w-2)", "cp": 2, "kod": 16, "red": -1, "normp": 5, "rootno": 1, "ord_cond": 1, "ord_disc": 12, "ord_den_j": 12}, {"p": "(-2*w+1)", "cp": 4, "kod": -5, "red": 0, "normp": 11, "rootno": -1, "ord_cond": 2, "ord_disc": 7, "ord_den_j": 1}], "analytic_rank": 1, "minD": "(568197411375*w-529685924625)", "label": "2.0.11.1-27225.5-d8", "jinv": "3533183376724708442/1427209716796875,1032777340820292487/1427209716796875", "conductor_label": "27225.5", "class_deg": 12, "reg": {"__RealLiteral__": 0, "data": "1.6612337525024385400958570641501268973", "prec": 130}, "class_size": 8, "class_label": "2.0.11.1-27225.5-d", "iso_label": "d", "degree": 2, "non_min_p": [], "q_curve": false, "short_label": "27225.5-d8", "short_class_label": "27225.5-d", "isogeny_matrix": [[1, 12, 12, 2, 4, 4, 6, 3], [12, 1, 4, 6, 3, 12, 2, 4], [12, 4, 1, 6, 12, 3, 2, 4], [2, 6, 6, 1, 2, 2, 3, 6], [4, 3, 12, 2, 1, 4, 6, 12], [4, 12, 3, 2, 4, 1, 6, 12], [6, 2, 2, 3, 6, 6, 1, 2], [3, 4, 4, 6, 12, 12, 2, 1]], "torsion_order": 2, "equation": "{y}^2+{x}{y}+\\left(a+1\\right){y}={x}^{3}+{x}^{2}+\\left(-545a+3138\\right){x}-27234a+3585", "gens": ["[[-7,28],[111,-51],[1,0]]"], "ngens": 1, "signature": [0, 1], "trace_hash": 844587199598426587, "heights": [{"__RealLiteral__": 0, "data": "1.6612337525024385400958570641501268973", "prec": 130}], "isodeg": [1, 2, 3, 4, 6, 12], "omega": {"__RealLiteral__": 0, "data": "0.13410632314018300215187745674494438122", "prec": 133}, "potential_good_reduction": false, "tamagawa_product": 48, "bad_primes": ["(-w)", "(w-1)", "(-w-1)", "(w-2)", "(-2*w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "3.2242217001666658998019367903086937141", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 5, "reducible_primes": [2, 3], "semistable": false, "disc": "(568197411375*w-529685924625)", "normdisc": 948145902411895751953125, "conductor_norm_factors": [3, 5, 11], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 3.8069473291421296, "cm_type": 0}