{"torsion_structure": [10], "ainvs": "1,0,0;0,-1,0;1,1,0;-11,15,-5;15,-31,12", "cm": 0, "torsion_gens": ["[[0,3,0],[3,-10,0],[1,0,0]]"], "number": 3, "rank": 0, "field_label": "3.3.49.1", "galois_images": ["2B", "5B.1.1"], "conductor_norm": 71, "abs_disc": 49, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "[71,71,4*w^2-3*w-5]", "base_change": [], "local_data": [{"p": "[71,71,4*w^2-3*w-5]", "cp": 2, "kod": "I_{2}", "red": 1, "normp": 71, "rootno": -1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 0, "minD": "[5041,5041,17*w^2-9*w-24]", "label": "3.3.49.1-71.1-a3", "jinv": "4240814798194/5041,1044582831031/5041,-1885779500418/5041", "conductor_label": "71.1", "class_deg": 10, "reg": 1, "class_size": 4, "isogeny_degrees": [1, 2, 5, 10], "class_label": "3.3.49.1-71.1-a", "iso_label": "a", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "71.1-a3", "short_class_label": "71.1-a", "isogeny_matrix": [[1, 2, 5, 10], [2, 1, 10, 5], [5, 10, 1, 2], [10, 5, 2, 1]], "torsion_order": 10, "non-surjective_primes": [2, 5], "equation": "\"y^2+xy+\\left(a+1\\right)y=x^{3}-ax^{2}+\\left(-5a^{2}+15a-11\\right)x+12a^{2}-31a+15\"", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 1967013989759310318, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "205.600454856667", "prec": 54}, "potential_good_reduction": false, "tamagawa_product": 2, "bad_primes": ["[71,71,4*w^2-3*w-5]"], "Lvalue": {"__RealLiteral__": 0, "data": "0.587429871019048", "prec": 57}, "sha": 1, "torsion_primes": [2, 5], "n_bad_primes": 1, "reducible_primes": [2, 5], "semistable": true}