{"torsion_structure": [3], "ainvs": "-1,-1,1,0,0;2,1,-1,0,0;-3,-6,4,2,-1;17,13,-19,-5,4;32,25,-37,-10,8", "cm": 0, "torsion_gens": ["[[0,0,0,0,0],[8,8,-9,-3,2],[1,0,0,0,0]]"], "number": 4, "rank": 0, "field_label": "5.5.65657.1", "galois_images": ["3B.1.1", "5B.4.1"], "conductor_norm": 45, "abs_disc": 65657, "iso_nlabel": 1, "rank_bounds": [0, 0], "conductor_ideal": "(w^3-4*w)", "base_change": [], "local_data": [{"p": "(-w^4+w^3+4*w^2-2*w-2)", "cp": 1, "kod": -1, "red": 0, "normp": 3, "rootno": -1, "ord_cond": 2, "ord_disc": 6, "ord_den_j": 0}, {"p": "(-w^2+w+2)", "cp": 1, "kod": 9, "red": -1, "normp": 5, "rootno": 1, "ord_cond": 1, "ord_disc": 5, "ord_den_j": 5}], "analytic_rank": 0, "minD": "(-12*w^4+21*w^3+34*w^2-44*w+1)", "label": "5.5.65657.1-45.1-b4", "jinv": "109010922/3125,393132181/3125,-300612723/3125,-143808649/3125,81829946/3125", "conductor_label": "45.1", "class_deg": 15, "reg": 1, "class_size": 4, "class_label": "5.5.65657.1-45.1-b", "iso_label": "b", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "45.1-b4", "short_class_label": "45.1-b", "isogeny_matrix": [[1, 3, 5, 15], [3, 1, 15, 5], [5, 15, 1, 3], [15, 5, 3, 1]], "torsion_order": 3, "equation": "{y}^2+\\left(a^{2}-a-1\\right){x}{y}+\\left(-a^{4}+2a^{3}+4a^{2}-6a-3\\right){y}={x}^{3}+\\left(-a^{2}+a+2\\right){x}^{2}+\\left(4a^{4}-5a^{3}-19a^{2}+13a+17\\right){x}+8a^{4}-10a^{3}-37a^{2}+25a+32", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 887817168432696360, "heights": [], "isodeg": [1, 3, 5, 15], "omega": {"__RealLiteral__": 0, "data": "3353.5057663780043173806752408540694671", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 1, "bad_primes": ["(-w^4+w^3+4*w^2-2*w-2)", "(-w^2+w+2)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.45417284", "prec": 34}, "sha": 1, "torsion_primes": [3], "n_bad_primes": 2, "reducible_primes": [3, 5], "semistable": false, "disc": "(-13*w^4+10*w^3+60*w^2-12*w-48)", "normdisc": -2278125, "conductor_norm_factors": [3, 5], "nonmax_primes": [3, 5], "nonmax_rad": 15, "root_analytic_conductor": 33.504282541262015, "cm_type": 0}