{"torsion_structure": [7], "ainvs": "0,-2,0,1,0;-1,-2,3,1,-1;1,-3,-3,1,1;1,1,-1,-1,0;-1,1,2,-1,-1", "cm": 0, "torsion_gens": ["[[2,-1,-5,1,2],[3,-3,-9,3,4],[1,0,0,0,0]]"], "number": 2, "rank": 0, "field_label": "5.5.14641.1", "galois_images": ["7B.1.1"], "conductor_norm": 43, "abs_disc": 14641, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(w^4+w^3-3*w^2-3*w+2)", "base_change": [], "local_data": [{"p": "(w^4+w^3-3*w^2-3*w+2)", "cp": 1, "kod": 5, "red": 1, "normp": 43, "rootno": -1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}], "analytic_rank": 0, "minD": "(w^4+w^3-3*w^2-3*w+2)", "label": "5.5.14641.1-43.4-a2", "jinv": "-354407213/43,1489970384/43,-730083346/43,-539160699/43,294508316/43", "conductor_label": "43.4", "class_deg": 7, "reg": 1, "class_size": 2, "class_label": "5.5.14641.1-43.4-a", "iso_label": "a", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "43.4-a2", "short_class_label": "43.4-a", "isogeny_matrix": [[1, 7], [7, 1]], "torsion_order": 7, "equation": "{y}^2+\\left(a^{3}-2a\\right){x}{y}+\\left(a^{4}+a^{3}-3a^{2}-3a+1\\right){y}={x}^{3}+\\left(-a^{4}+a^{3}+3a^{2}-2a-1\\right){x}^{2}+\\left(-a^{3}-a^{2}+a+1\\right){x}-a^{4}-a^{3}+2a^{2}+a-1", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 1046838870332134748, "heights": [], "isodeg": [1, 7], "omega": {"__RealLiteral__": 0, "data": "5702.6939771777020275064320793350236517", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 1, "bad_primes": ["(w^4+w^3-3*w^2-3*w+2)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.961830659", "prec": 37}, "sha": 1, "torsion_primes": [7], "n_bad_primes": 1, "reducible_primes": [7], "semistable": true, "disc": "(-w^4+2*w^3+2*w^2-5*w)", "normdisc": -43, "conductor_norm_factors": [43], "nonmax_primes": [7], "nonmax_rad": 7, "root_analytic_conductor": 15.749645008192008, "cm_type": 0}