{"torsion_structure": [2], "ainvs": "0,0;-1,0;0,0;-1,16;-31,-16", "cm": 0, "torsion_gens": ["[[3,-2],[0,0],[1,0]]"], "number": 3, "rank": 1, "field_label": "2.0.7.1", "galois_images": ["2B"], "conductor_norm": 28672, "abs_disc": 7, "iso_nlabel": 17, "rank_bounds": [1, 1], "conductor_ideal": "(-128*w+64)", "base_change": [], "local_data": [{"p": "(w)", "cp": 4, "kod": -9, "red": 0, "normp": 2, "rootno": 1, "ord_cond": 6, "ord_disc": 15, "ord_den_j": 0}, {"p": "(-w+1)", "cp": 4, "kod": -8, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 6, "ord_disc": 14, "ord_den_j": 0}, {"p": "(-2*w+1)", "cp": 1, "kod": 5, "red": 1, "normp": 7, "rootno": -1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}], "analytic_rank": 1, "minD": "(16384*w-65536)", "label": "2.0.7.1-28672.7-r3", "jinv": "28248/7,88712/7", "conductor_label": "28672.7", "class_deg": 4, "reg": {"__RealLiteral__": 0, "data": "0.43737684447033311959559062425713467889", "prec": 133}, "class_size": 4, "class_label": "2.0.7.1-28672.7-r", "iso_label": "r", "degree": 2, "non_min_p": [], "q_curve": false, "short_label": "28672.7-r3", "short_class_label": "28672.7-r", "isogeny_matrix": [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], "torsion_order": 2, "equation": "{y}^2={x}^{3}-{x}^{2}+\\left(16a-1\\right){x}-16a-31", "gens": ["[[-3,0],[8,-8],[1,0]]"], "ngens": 1, "signature": [0, 1], "trace_hash": 1612404768154748520, "heights": [{"__RealLiteral__": 0, "data": "0.43737684447033311959559062425713467889", "prec": 133}], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "1.9060249456570229530889424510037488662", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 16, "bad_primes": ["(w)", "(-w+1)", "(-2*w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "5.0414484398551545112676965645083479427", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 3, "reducible_primes": [2], "semistable": false, "disc": "(-16384*w+65536)", "normdisc": 3758096384, "conductor_norm_factors": [2, 7], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 3.076465650952455, "cm_type": 0}