{"torsion_structure": [9], "ainvs": "0,0,0;-1,0,1;1,1,0;-53,-3,17;164,17,-56", "cm": -27, "torsion_gens": ["[[-2,-1,1],[-17,-3,6],[1,0,0]]"], "number": 3, "field_label": "3.3.81.1", "galois_images": ["3B.1.1"], "conductor_norm": 27, "abs_disc": 81, "iso_nlabel": 0, "conductor_ideal": "[27,3,3]", "base_change": ["27.a2"], "local_data": [{"ord_disc": 3, "ord_cond": 3, "normp": 3, "kod": "II", "rootno": -1, "p": "[3,3,w^2-1]", "ord_den_j": 0, "cp": 1, "red": 0}], "minD": "[27,3,3]", "label": "3.3.81.1-27.1-a3", "jinv": "-12288000,0,0", "conductor_label": "27.1", "class_deg": 27, "reg": 1, "class_size": 4, "isogeny_degrees": [1, 3, 9, 27], "class_label": "3.3.81.1-27.1-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": true, "short_label": "27.1-a3", "short_class_label": "27.1-a", "torsion_order": 9, "non-surjective_primes": [3], "equation": "\" y^2 + \\left(a + 1\\right) y = x^{3} + \\left(a^{2} - 1\\right) x^{2} + \\left(17 a^{2} - 3 a - 53\\right) x - 56 a^{2} + 17 a + 164  \"", "old_heights": [], "signature": [3, 0]}