{"torsion_structure": [2], "ainvs": "-1,-1,1,0;-3,3,2,-1;-2,-1,1,0;451,-799,-345,255;-21549,18463,11701,-6627", "cm": 0, "torsion_gens": ["[[25/2,-99/4,-19/2,15/2],[-9/4,-23/8,-9/8,9/8],[1,0,0,0]]"], "number": 4, "rank": 0, "field_label": "4.4.2777.1", "galois_images": ["2B", "3B.1.2"], "conductor_norm": 22, "abs_disc": 2777, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(-w^3+3*w)", "base_change": [], "local_data": [{"p": "(-w)", "cp": 2, "kod": 52, "red": -1, "normp": 2, "rootno": 1, "ord_cond": 1, "ord_disc": 48, "ord_den_j": 48}, {"p": "(-w^3+2*w^2+2*w-1)", "cp": 2, "kod": 10, "red": -1, "normp": 11, "rootno": 1, "ord_cond": 1, "ord_disc": 6, "ord_den_j": 6}], "analytic_rank": 0, "minD": "(-76805*w^3+114298*w^2+266050*w-45660)", "label": "4.4.2777.1-22.1-a4", "jinv": "3638403917729845697875388025793/498650091216506454016,3112599543413066339294706687465/249325045608253227008,261719896030458847171340772313/498650091216506454016,-1502268147076192175039019336779/498650091216506454016", "conductor_label": "22.1", "class_deg": 24, "reg": 1, "class_size": 12, "class_label": "4.4.2777.1-22.1-a", "iso_label": "a", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "22.1-a4", "short_class_label": "22.1-a", "isogeny_matrix": [[1, 2, 4, 12, 6, 2, 4, 3, 6, 12, 6, 2], [2, 1, 8, 24, 12, 4, 8, 6, 3, 24, 12, 4], [4, 8, 1, 3, 24, 8, 4, 12, 24, 12, 6, 2], [12, 24, 3, 1, 8, 24, 12, 4, 8, 4, 2, 6], [6, 12, 24, 8, 1, 3, 24, 2, 4, 8, 4, 12], [2, 4, 8, 24, 3, 1, 8, 6, 12, 24, 12, 4], [4, 8, 4, 12, 24, 8, 1, 12, 24, 3, 6, 2], [3, 6, 12, 4, 2, 6, 12, 1, 2, 4, 2, 6], [6, 3, 24, 8, 4, 12, 24, 2, 1, 8, 4, 12], [12, 24, 12, 4, 8, 24, 3, 4, 8, 1, 2, 6], [6, 12, 6, 2, 4, 12, 6, 2, 4, 2, 1, 3], [2, 4, 2, 6, 12, 4, 2, 6, 12, 6, 3, 1]], "torsion_order": 2, "equation": "{y}^2+\\left(a^{2}-a-1\\right){x}{y}+\\left(a^{2}-a-2\\right){y}={x}^{3}+\\left(-a^{3}+2a^{2}+3a-3\\right){x}^{2}+\\left(255a^{3}-345a^{2}-799a+451\\right){x}-6627a^{3}+11701a^{2}+18463a-21549", "gens": [], "ngens": 0, "signature": [4, 0], "trace_hash": 74456722157883013, "heights": [], "isodeg": [1, 2, 3, 4, 6, 8, 12, 24], "omega": {"__RealLiteral__": 0, "data": "4.9279349520765874345145353311295468223", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 4, "bad_primes": ["(-w)", "(-w^3+2*w^2+2*w-1)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.841626760920221", "prec": 57}, "sha": 9, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2, 3], "semistable": true, "disc": "(-76805*w^3+114298*w^2+266050*w-45660)", "normdisc": 498650091216506454016, "conductor_norm_factors": [2, 11], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 6.929937670547061, "cm_type": 0}