{"torsion_structure": [], "ainvs": "-3,-3,5,1,-1;-2,0,5,0,-1;-1,-4,0,1,0;-937,-1670,662,1330,-527;27660,47105,-28524,-41440,18278", "cm": 0, "torsion_gens": [], "number": 1, "rank": 0, "field_label": "5.5.65657.1", "galois_images": ["3B.1.2", "5B.4.2"], "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": 7, "red": -1, "normp": 5, "rootno": 1, "ord_cond": 1, "ord_disc": 3, "ord_den_j": 3}], "analytic_rank": 0, "minD": "(-6*w^4+9*w^3+28*w^2-23*w-17)", "label": "5.5.65657.1-45.1-b1", "jinv": "-6711393728551335750914883813930912798473/125,-38438451731868504360194666541225269140904/125,-41380713886380859304809564621687978514293/125,3459009377990835094505717267240191015816/125,9227278873526453906244312610219036327836/125", "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-b1", "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": 1, "equation": "{y}^2+\\left(-a^{4}+a^{3}+5a^{2}-3a-3\\right){x}{y}+\\left(a^{3}-4a-1\\right){y}={x}^{3}+\\left(-a^{4}+5a^{2}-2\\right){x}^{2}+\\left(-527a^{4}+1330a^{3}+662a^{2}-1670a-937\\right){x}+18278a^{4}-41440a^{3}-28524a^{2}+47105a+27660", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 887817168432696360, "heights": [], "isodeg": [1, 3, 5, 15], "omega": {"__RealLiteral__": 0, "data": "1.6560522303101255888299630819032441813", "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": 225, "torsion_primes": [], "n_bad_primes": 2, "reducible_primes": [3, 5], "semistable": false, "disc": "(6*w^4-9*w^3-28*w^2+23*w+17)", "normdisc": -91125, "conductor_norm_factors": [3, 5], "nonmax_primes": [3, 5], "nonmax_rad": 15, "root_analytic_conductor": 33.504282541262015, "cm_type": 0}