{"torsion_structure": [2], "ainvs": "1,0;1,0;0,0;44,0;55,0", "cm": 0, "torsion_gens": ["[[-5/4,0],[5/8,0],[1,0]]"], "number": 2, "rank": 1, "field_label": "2.2.33.1", "galois_images": ["2B"], "conductor_norm": 33, "abs_disc": 33, "iso_nlabel": 0, "rank_bounds": [1, 1], "conductor_ideal": "(-2*w+1)", "base_change": ["33.a4", "1089.j4"], "local_data": [{"p": "(-2*w+7)", "cp": 2, "kod": 28, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 24, "ord_den_j": 24}, {"p": "(-4*w-9)", "cp": 2, "kod": 6, "red": 1, "normp": 11, "rootno": -1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 1, "minD": "(5845851)", "label": "2.2.33.1-33.1-a2", "jinv": "9090072503/5845851,0", "conductor_label": "33.1", "class_deg": 8, "reg": {"__RealLiteral__": 0, "data": "2.9577010044811001071227173060498724674", "prec": 130}, "class_size": 6, "class_label": "2.2.33.1-33.1-a", "iso_label": "a", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "33.1-a2", "short_class_label": "33.1-a", "isogeny_matrix": [[1, 8, 4, 2, 8, 4], [8, 1, 2, 4, 4, 8], [4, 2, 1, 2, 2, 4], [2, 4, 2, 1, 4, 2], [8, 4, 2, 4, 1, 8], [4, 8, 4, 2, 8, 1]], "torsion_order": 2, "equation": "{y}^2+{x}{y}={x}^{3}+{x}^{2}+44{x}+55", "gens": ["[[11/4,0],[-31/8,5],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 2125200354529643087, "heights": [{"__RealLiteral__": 0, "data": "2.9577010044811001071227173060498724674", "prec": 130}], "isodeg": [1, 2, 4, 8], "omega": {"__RealLiteral__": 0, "data": "2.2340632069954015022360997243286296108", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 4, "bad_primes": ["(-2*w+7)", "(-4*w-9)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.3005027181265763143156656624447302351", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2], "semistable": true, "disc": "(-5845851)", "normdisc": 34173973914201, "conductor_norm_factors": [3, 11], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 1.2303367836963277, "cm_type": 0}