{"torsion_structure": [6], "ainvs": "1,1;0,0;1,1;1,1;2,1", "cm": 0, "torsion_gens": ["[[3,1],[4,1],[1,0]]"], "number": 1, "rank": 1, "field_label": "2.2.85.1", "galois_images": ["2B", "3B.1.1"], "conductor_norm": 3, "abs_disc": 85, "iso_nlabel": 1, "rank_bounds": [1, 1], "conductor_ideal": "(3,w)", "base_change": [], "local_data": [{"p": "(3,w)", "cp": 6, "kod": 10, "red": 1, "normp": 3, "rootno": -1, "ord_cond": 1, "ord_disc": 6, "ord_den_j": 6}], "analytic_rank": 1, "minD": "(5*w+33)", "label": "2.2.85.1-3.1-b1", "jinv": "3864485/729,-505895/729", "conductor_label": "3.1", "class_deg": 6, "reg": {"__RealLiteral__": 0, "data": "1.3575042638898117315433699319184806524", "prec": 130}, "class_size": 4, "class_label": "2.2.85.1-3.1-b", "iso_label": "b", "degree": 2, "non_min_p": [], "q_curve": false, "short_label": "3.1-b1", "short_class_label": "3.1-b", "isogeny_matrix": [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], "torsion_order": 6, "equation": "{y}^2+\\left(a+1\\right){x}{y}+\\left(a+1\\right){y}={x}^{3}+\\left(a+1\\right){x}+a+2", "gens": ["[[6,-2],[-14,5],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 498287141824628858, "heights": [{"__RealLiteral__": 0, "data": "1.3575042638898117315433699319184806524", "prec": 130}], "isodeg": [1, 2, 3, 6], "omega": {"__RealLiteral__": 0, "data": "25.180551277512858329797330283161802549", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 6, "bad_primes": ["(3,w)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.2358783337818239273938172281761347969", "prec": 130}, "sha": 1, "torsion_primes": [2, 3], "n_bad_primes": 1, "reducible_primes": [2, 3], "semistable": true, "disc": "(5*w+33)", "normdisc": 729, "conductor_norm_factors": [3], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 1.084247251828703, "cm_type": 0}