{"torsion_structure": [2], "ainvs": "1,1;1,0;1,0;233,-361;-5056,1708", "cm": 0, "torsion_gens": ["[[7/2,21/4],[45/8,-7],[1,0]]"], "number": 5, "rank": 2, "field_label": "2.0.11.1", "galois_images": ["2B", "3B"], "conductor_norm": 27225, "abs_disc": 11, "iso_nlabel": 1, "rank_bounds": [2, 2], "conductor_ideal": "(165)", "base_change": [], "local_data": [{"p": "(-w)", "cp": 2, "kod": 8, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}, {"p": "(w-1)", "cp": 1, "kod": 7, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 3, "ord_den_j": 3}, {"p": "(-w-1)", "cp": 2, "kod": 16, "red": -1, "normp": 5, "rootno": 1, "ord_cond": 1, "ord_disc": 12, "ord_den_j": 12}, {"p": "(w-2)", "cp": 1, "kod": 5, "red": -1, "normp": 5, "rootno": 1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}, {"p": "(-2*w+1)", "cp": 2, "kod": -1, "red": 0, "normp": 11, "rootno": -1, "ord_cond": 2, "ord_disc": 6, "ord_den_j": 0}], "analytic_rank": 2, "minD": "(-1133273295*w-527734845)", "label": "2.0.11.1-27225.5-b5", "jinv": "105891919018084/19775390625,93926997067673/19775390625", "conductor_label": "27225.5", "class_deg": 12, "reg": {"__RealLiteral__": 0, "data": "3.0482654482955999076896697797841216553", "prec": 130}, "class_size": 8, "class_label": "2.0.11.1-27225.5-b", "iso_label": "b", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "27225.5-b5", "short_class_label": "27225.5-b", "isogeny_matrix": [[1, 3, 2, 6, 12, 4, 12, 4], [3, 1, 6, 2, 4, 12, 4, 12], [2, 6, 1, 3, 6, 2, 6, 2], [6, 2, 3, 1, 2, 6, 2, 6], [12, 4, 6, 2, 1, 12, 4, 3], [4, 12, 2, 6, 12, 1, 3, 4], [12, 4, 6, 2, 4, 3, 1, 12], [4, 12, 2, 6, 3, 4, 12, 1]], "torsion_order": 2, "equation": "{y}^2+\\left(a+1\\right){x}{y}+{y}={x}^{3}+{x}^{2}+\\left(-361a+233\\right){x}+1708a-5056", "gens": ["[[-43/3,-62/9],[83/9,-1355/27],[1,0]]", "[[-13,-14],[-81,26],[1,0]]"], "ngens": 2, "signature": [0, 1], "trace_hash": 261608240737180898, "heights": [{"__RealLiteral__": 0, "data": "1.7737080913251669667109457682060798264", "prec": 130}, {"__RealLiteral__": 0, "data": "2.0391995734925046641927612801372850402", "prec": 130}], "isodeg": [1, 2, 3, 4, 6, 12], "omega": {"__RealLiteral__": 0, "data": "0.34525060569987996616163764342625378984", "prec": 133}, "potential_good_reduction": false, "tamagawa_product": 8, "bad_primes": ["(-w)", "(w-1)", "(-w-1)", "(w-2)", "(-2*w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "5.0770433624856225136592855125940239549", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 5, "reducible_primes": [2, 3], "semistable": false, "disc": "(-1133273295*w-527734845)", "normdisc": 4729496956787109375, "conductor_norm_factors": [3, 5, 11], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 3.8069473291421296, "cm_type": 0}