{"torsion_structure": [2], "ainvs": "1,0;0,1;1,1;-133045221,-22765000;-1761877861908,-301470021617", "cm": 0, "torsion_gens": ["[[9943,1701],[-4972,-851],[1,0]]"], "number": 2, "rank": 2, "field_label": "2.2.161.1", "galois_images": ["2B", "3B"], "conductor_norm": 28, "abs_disc": 161, "iso_nlabel": 4, "rank_bounds": [2, 2], "conductor_ideal": "(-64*w+438)", "base_change": ["7406.a5", "98.a5"], "local_data": [{"p": "(w+6)", "cp": 2, "kod": 6, "red": -1, "normp": 2, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}, {"p": "(-w+7)", "cp": 2, "kod": 6, "red": -1, "normp": 2, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}, {"p": "(-32*w+219)", "cp": 2, "kod": 6, "red": -1, "normp": 7, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 2, "minD": "(28)", "label": "2.2.161.1-28.1-e2", "jinv": "-15625/28,0", "conductor_label": "28.1", "class_deg": 18, "reg": {"__RealLiteral__": 0, "data": "0.69754299240873810072361697932065431366", "prec": 133}, "class_size": 6, "class_label": "2.2.161.1-28.1-e", "iso_label": "e", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "28.1-e2", "short_class_label": "28.1-e", "isogeny_matrix": [[1, 9, 3, 6, 18, 2], [9, 1, 3, 6, 2, 18], [3, 3, 1, 2, 6, 6], [6, 6, 2, 1, 3, 3], [18, 2, 6, 3, 1, 9], [2, 18, 6, 3, 9, 1]], "torsion_order": 2, "equation": "{y}^2+{x}{y}+\\left(a+1\\right){y}={x}^{3}+a{x}^{2}+\\left(-22765000a-133045221\\right){x}-301470021617a-1761877861908", "gens": ["[[63155/4,10805/4],[18924643/8,3238141/8],[1,0]]", "[[20790,3557],[-4001922,-684758],[1,0]]"], "ngens": 2, "signature": [2, 0], "trace_hash": 1467585782260396737, "heights": [{"__RealLiteral__": 0, "data": "1.1824091302551704334461777285696064619", "prec": 130}, {"__RealLiteral__": 0, "data": "0.87798658204026519060156887146128309182", "prec": 133}], "isodeg": [1, 2, 3, 6, 9, 18], "omega": {"__RealLiteral__": 0, "data": "7.0277081059000617705423007125374356141", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 8, "bad_primes": ["(w+6)", "(-w+7)", "(-32*w+219)"], "Lvalue": {"__RealLiteral__": 0, "data": "3.0907348133152554895508027077027671895", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 3, "reducible_primes": [2, 3], "semistable": true, "disc": "(-28)", "normdisc": 784, "conductor_norm_factors": [2, 7], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 2.6082006533137285, "cm_type": 0}