{"torsion_structure": [2], "ainvs": "0,0;0,-1;0,0;-299,-170;2958,1711", "cm": -48, "torsion_gens": ["[[6,5],[0,0],[1,0]]"], "number": 7, "rank": 1, "field_label": "2.2.12.1", "galois_images": [], "conductor_norm": 1024, "abs_disc": 12, "iso_nlabel": 9, "rank_bounds": [1, 1], "conductor_ideal": "(32)", "base_change": [], "local_data": [{"p": "(w+1)", "cp": 4, "kod": -16, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 10, "ord_disc": 26, "ord_den_j": 0}], "analytic_rank": 1, "minD": "(8192)", "label": "2.2.12.1-1024.1-j7", "jinv": "1417905000,818626500", "conductor_label": "1024.1", "class_deg": 12, "reg": {"__RealLiteral__": 0, "data": "0.42995748788770280185660727099930178056", "prec": 133}, "class_size": 8, "class_label": "2.2.12.1-1024.1-j", "iso_label": "j", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "1024.1-j7", "short_class_label": "1024.1-j", "isogeny_matrix": [[1, 3, 4, 12, 2, 6, 4, 12], [3, 1, 12, 4, 6, 2, 12, 4], [4, 12, 1, 12, 2, 6, 4, 3], [12, 4, 12, 1, 6, 2, 3, 4], [2, 6, 2, 6, 1, 3, 2, 6], [6, 2, 6, 2, 3, 1, 6, 2], [4, 12, 4, 3, 2, 6, 1, 12], [12, 4, 3, 4, 6, 2, 12, 1]], "torsion_order": 2, "equation": "{y}^2={x}^{3}-a{x}^{2}+\\left(-170a-299\\right){x}+1711a+2958", "gens": ["[[9,2],[0,8],[1,0]]"], "ngens": 1, "signature": [2, 0], "trace_hash": 2088616481465853177, "heights": [{"__RealLiteral__": 0, "data": "0.42995748788770280185660727099930178056", "prec": 133}], "isodeg": [1, 2, 3, 4, 6, 12], "omega": {"__RealLiteral__": 0, "data": "10.835949789494969070196421559922294062", "prec": 130}, "potential_good_reduction": true, "tamagawa_product": 4, "bad_primes": ["(w+1)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.6898736053291367872363019576189107287", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2, 3], "semistable": false, "disc": "(8192)", "normdisc": 67108864, "conductor_norm_factors": [2], "nonmax_primes": [], "nonmax_rad": 1, "root_analytic_conductor": 1.7510726534376486, "cm_type": -1}