{"torsion_structure": [6], "ainvs": "-5,0,1;5,0,-1;0,0,0;-3,29,-11;133,-146,37", "cm": 0, "torsion_gens": ["[[-2,1,0],[7,-8,2],[1,0,0]]"], "number": 4, "rank": 1, "field_label": "3.3.733.1", "galois_images": ["2B", "3B.1.1"], "conductor_norm": 2, "abs_disc": 733, "iso_nlabel": 1, "rank_bounds": [1, 1], "conductor_ideal": "(w^2-6)", "base_change": [], "local_data": [{"p": "(w^2-6)", "cp": 2, "kod": 16, "red": -1, "normp": 2, "rootno": 1, "ord_cond": 1, "ord_disc": 12, "ord_den_j": 12}], "analytic_rank": 1, "minD": "(w^2+8*w)", "label": "3.3.733.1-2.1-b4", "jinv": "12352857/4096,-11083745/4096,2615577/4096", "conductor_label": "2.1", "class_deg": 6, "reg": {"__RealLiteral__": 0, "data": "1.1008579324817441694229838748377948570", "prec": 130}, "class_size": 4, "class_label": "3.3.733.1-2.1-b", "iso_label": "b", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "2.1-b4", "short_class_label": "2.1-b", "isogeny_matrix": [[1, 3, 2, 6], [3, 1, 6, 2], [2, 6, 1, 3], [6, 2, 3, 1]], "torsion_order": 6, "equation": "{y}^2+\\left(a^{2}-5\\right){x}{y}={x}^{3}+\\left(-a^{2}+5\\right){x}^{2}+\\left(-11a^{2}+29a-3\\right){x}+37a^{2}-146a+133", "gens": ["[[8,-7/4,-1/2],[-16,17/8,13/8],[1,0,0]]"], "ngens": 1, "signature": [3, 0], "trace_hash": 1035800401786627869, "heights": [{"__RealLiteral__": 0, "data": "1.1008579324817441694229838748377948570", "prec": 130}], "isodeg": [1, 2, 3, 6], "omega": {"__RealLiteral__": 0, "data": "125.94591391463178512125553717886865961", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["(w^2-6)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.85351689191865735834263246428729022860", "prec": 133}, "sha": 1, "torsion_primes": [2, 3], "n_bad_primes": 1, "reducible_primes": [2, 3], "semistable": true, "disc": "(-w^2-8*w)", "normdisc": 4096, "conductor_norm_factors": [2], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 2.7155775319800473, "cm_type": 0}