{"torsion_structure": [3], "ainvs": "-4,-1,1,0;0,1,0,0;-5,-5,0,1;-51,-147,-28,29;-287,-206,63,12", "cm": 0, "torsion_gens": ["[[11,12,1,-2],[-8,-28,-4,5],[1,0,0,0]]"], "number": 3, "rank": 1, "field_label": "4.4.10512.1", "galois_images": ["3Cs.1.1", "5B.4.2"], "conductor_norm": 4, "abs_disc": 10512, "iso_nlabel": 0, "rank_bounds": [1, 1], "conductor_ideal": "(w^3-w^2-5*w)", "base_change": [], "local_data": [{"p": "(w^3-w^2-5*w)", "cp": 15, "kod": 19, "red": 1, "normp": 4, "rootno": -1, "ord_cond": 1, "ord_disc": 15, "ord_den_j": 15}], "analytic_rank": 1, "minD": "(128*w^3-128*w^2-640*w)", "label": "4.4.10512.1-4.1-a3", "jinv": "90950209108247/32,1331603480023305/256,266320696004661/256,-266320696004661/256", "conductor_label": "4.1", "class_deg": 45, "reg": {"__RealLiteral__": 0, "data": "1.0758218114330386365153533349269547945", "prec": 130}, "class_size": 6, "class_label": "4.4.10512.1-4.1-a", "iso_label": "a", "degree": 4, "non_min_p": [], "q_curve": false, "short_label": "4.1-a3", "short_class_label": "4.1-a", "isogeny_matrix": [[1, 5, 3, 45, 15, 9], [5, 1, 15, 9, 3, 45], [3, 15, 1, 15, 5, 3], [45, 9, 15, 1, 3, 5], [15, 3, 5, 3, 1, 15], [9, 45, 3, 5, 15, 1]], "torsion_order": 3, "equation": "{y}^2+\\left(a^{2}-a-4\\right){x}{y}+\\left(a^{3}-5a-5\\right){y}={x}^{3}+a{x}^{2}+\\left(29a^{3}-28a^{2}-147a-51\\right){x}+12a^{3}+63a^{2}-206a-287", "gens": ["[[-302029/64009,-662608/64009,-3771/64009,90202/64009],[-57679796/16194277,-702015104/16194277,-141522592/16194277,121612401/16194277],[1,0,0,0]]"], "ngens": 1, "signature": [4, 0], "trace_hash": 1906871495863787605, "heights": [{"__RealLiteral__": 0, "data": "1.0758218114330386365153533349269547945", "prec": 130}], "isodeg": [1, 3, 5, 15], "omega": {"__RealLiteral__": 0, "data": "28.659471545381856813935013773342846714", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 15, "bad_primes": ["(w^3-w^2-5*w)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.00481631535149", "prec": 54}, "sha": 1, "torsion_primes": [3], "n_bad_primes": 1, "reducible_primes": [3, 5], "semistable": true, "disc": "(128*w^3-128*w^2-640*w)", "normdisc": 1073741824, "conductor_norm_factors": [2], "nonmax_primes": [3, 5], "nonmax_rad": 15, "root_analytic_conductor": 10.895288348649155, "cm_type": 0}