{"torsion_structure": [12], "ainvs": "-1,0,1;1,-1,0;-2,1,1;21,43,-30;-66,-160,103", "cm": 0, "torsion_gens": ["[[17,4,-7],[-53,3,13],[1,0,0]]"], "number": 1, "rank": 0, "field_label": "3.3.81.1", "galois_images": ["2B", "3B.1.1"], "conductor_norm": 17, "abs_disc": 81, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(w^2+w-3)", "base_change": [], "local_data": [{"p": "(w^2+w-3)", "cp": 3, "kod": 7, "red": 1, "normp": 17, "rootno": -1, "ord_cond": 1, "ord_disc": 3, "ord_den_j": 3}], "analytic_rank": 0, "minD": "(-3*w^2-2*w-12)", "label": "3.3.81.1-17.2-a1", "jinv": "43312806/4913,127953099/4913,42561684/4913", "conductor_label": "17.2", "class_deg": 12, "reg": 1, "class_size": 8, "class_label": "3.3.81.1-17.2-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "17.2-a1", "short_class_label": "17.2-a", "isogeny_matrix": [[1, 4, 2, 4, 12, 6, 3, 12], [4, 1, 2, 4, 12, 6, 12, 3], [2, 2, 1, 2, 6, 3, 6, 6], [4, 4, 2, 1, 3, 6, 12, 12], [12, 12, 6, 3, 1, 2, 4, 4], [6, 6, 3, 6, 2, 1, 2, 2], [3, 12, 6, 12, 4, 2, 1, 4], [12, 3, 6, 12, 4, 2, 4, 1]], "torsion_order": 12, "equation": "{y}^2+\\left(a^{2}-1\\right){x}{y}+\\left(a^{2}+a-2\\right){y}={x}^{3}+\\left(-a+1\\right){x}^{2}+\\left(-30a^{2}+43a+21\\right){x}+103a^{2}-160a-66", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 1751740446715663074, "heights": [], "isodeg": [1, 2, 3, 4, 6, 12], "omega": {"__RealLiteral__": 0, "data": "219.13785712855616235688770900708778259", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 3, "bad_primes": ["(w^2+w-3)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.50726355816795407952983265973862912638", "prec": 133}, "sha": 1, "torsion_primes": [2, 3], "n_bad_primes": 1, "reducible_primes": [2, 3], "semistable": true, "disc": "(-13*w^2+16*w+25)", "normdisc": 4913, "conductor_norm_factors": [17], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 1.2896025498827992, "cm_type": 0}