{"torsion_structure": [2], "ainvs": "1,1,0;6,0,-1;-4,1,1;28,-6,-6;33,-12,-9", "cm": 0, "torsion_gens": ["[[-1/4,-3/4,-1/4],[9/8,7/8,1/8],[1,0,0]]"], "number": 2, "rank": 1, "field_label": "3.3.733.1", "galois_images": ["2B"], "conductor_norm": 4, "abs_disc": 733, "iso_nlabel": 0, "rank_bounds": [1, 1], "conductor_ideal": "(w^2+w-3)", "base_change": [], "local_data": [{"p": "(w^2+w-3)", "cp": 2, "kod": 6, "red": -1, "normp": 4, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 1, "minD": "(w^2-w-3)", "label": "3.3.733.1-4.1-a2", "jinv": "-16431,39469/4,23323/4", "conductor_label": "4.1", "class_deg": 2, "reg": {"__RealLiteral__": 0, "data": "0.084974822910229672115725698213082368917", "prec": 137}, "class_size": 2, "class_label": "3.3.733.1-4.1-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "4.1-a2", "short_class_label": "4.1-a", "isogeny_matrix": [[1, 2], [2, 1]], "torsion_order": 2, "equation": "{y}^2+\\left(a+1\\right){x}{y}+\\left(a^{2}+a-4\\right){y}={x}^{3}+\\left(-a^{2}+6\\right){x}^{2}+\\left(-6a^{2}-6a+28\\right){x}-9a^{2}-12a+33", "gens": ["[[-11,4,3],[56,-25,-17],[1,0,0]]"], "ngens": 1, "signature": [3, 0], "trace_hash": 1063099870828433470, "heights": [{"__RealLiteral__": 0, "data": "0.084974822910229672115725698213082368917", "prec": 137}], "isodeg": [1, 2], "omega": {"__RealLiteral__": 0, "data": "211.00862856245316054549156674898921478", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(w^2+w-3)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.99341280734349055405285445459018112470", "prec": 133}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2], "semistable": true, "disc": "(w^2-w-3)", "normdisc": -16, "conductor_norm_factors": [2], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 3.048132718889235, "cm_type": 0}