{"torsion_structure": [2], "ainvs": "3,1,-4,0,1;-1,-4,1,1,0;3,1,-4,0,1;-1191,-609,1434,226,-372;-16315,-7895,20110,2964,-5104", "cm": 0, "torsion_gens": ["[[-23,-2,40,0,-10],[29,11,-41,-5,12],[1,0,0,0,0]]"], "number": 4, "rank": 0, "field_label": "5.5.14641.1", "galois_images": ["2B", "5B.1.2"], "conductor_norm": 23, "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": 23, "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": "5.5.14641.1-23.3-a4", "jinv": "127932477431619398226629/23,65672136847671723793825/23,-153067823422492698650307/23,-26048650375034470290668/23,36413212515684578678223/23", "conductor_label": "23.3", "class_deg": 10, "reg": 1, "class_size": 4, "class_label": "5.5.14641.1-23.3-a", "iso_label": "a", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "23.3-a4", "short_class_label": "23.3-a", "isogeny_matrix": [[1, 5, 10, 2], [5, 1, 2, 10], [10, 2, 1, 5], [2, 10, 5, 1]], "torsion_order": 2, "equation": "{y}^2+\\left(a^{4}-4a^{2}+a+3\\right){x}{y}+\\left(a^{4}-4a^{2}+a+3\\right){y}={x}^{3}+\\left(a^{3}+a^{2}-4a-1\\right){x}^{2}+\\left(-372a^{4}+226a^{3}+1434a^{2}-609a-1191\\right){x}-5104a^{4}+2964a^{3}+20110a^{2}-7895a-16315", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 1894256519342967484, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "0.63560068287913830074068320450643465998", "prec": 133}, "potential_good_reduction": false, "tamagawa_product": 1, "bad_primes": ["(-w^4+w^3+3*w^2-3*w-2)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.820765345", "prec": 37}, "sha": 625, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2, 5], "semistable": true, "disc": "(w^4-w^3-3*w^2+3*w+2)", "normdisc": -23, "conductor_norm_factors": [23], "nonmax_primes": [2, 5], "nonmax_rad": 10, "root_analytic_conductor": 14.794377883723698, "cm_type": 0}