{"torsion_structure": [4], "ainvs": "0,0;1,0;0,0;-21504,0;-1220940,0", "cm": 0, "torsion_gens": ["[[-84,0],[6,-12],[1,0]]"], "number": 8, "rank": 1, "field_label": "2.0.7.1", "galois_images": ["2B"], "conductor_norm": 16128, "abs_disc": 7, "iso_nlabel": 13, "rank_bounds": [1, 1], "conductor_ideal": "(-96*w+48)", "base_change": ["336.d1", "2352.l1"], "local_data": [{"p": "(w)", "cp": 2, "kod": -10, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 4, "ord_disc": 14, "ord_den_j": 2}, {"p": "(-w+1)", "cp": 2, "kod": -10, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 4, "ord_disc": 14, "ord_den_j": 2}, {"p": "(-2*w+1)", "cp": 2, "kod": 6, "red": 1, "normp": 7, "rootno": -1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}, {"p": "(3)", "cp": 2, "kod": 6, "red": 1, "normp": 9, "rootno": -1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 1, "minD": "(1032192)", "label": "2.0.7.1-16128.5-n8", "jinv": "268498407453697/252,0", "conductor_label": "16128.5", "class_deg": 16, "reg": {"__RealLiteral__": 0, "data": "4.6216236294138492274052141750636641972", "prec": 130}, "class_size": 8, "class_label": "2.0.7.1-16128.5-n", "iso_label": "n", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "16128.5-n8", "short_class_label": "16128.5-n", "isogeny_matrix": [[1, 2, 4, 16, 8, 16, 4, 8], [2, 1, 2, 8, 4, 8, 2, 4], [4, 2, 1, 16, 8, 16, 4, 8], [16, 8, 16, 1, 2, 4, 4, 8], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [4, 2, 4, 4, 2, 4, 1, 2], [8, 4, 8, 8, 4, 8, 2, 1]], "torsion_order": 4, "equation": "{y}^2={x}^{3}+{x}^{2}-21504{x}-1220940", "gens": ["[[-14876/175,0],[-274/6125,548/6125],[1,0]]"], "ngens": 1, "signature": [0, 1], "trace_hash": 665853416593839982, "heights": [{"__RealLiteral__": 0, "data": "4.6216236294138492274052141750636641972", "prec": 130}], "isodeg": [1, 2, 4, 8], "omega": {"__RealLiteral__": 0, "data": "0.17127295826650363689806119888102615669", "prec": 133}, "potential_good_reduction": false, "tamagawa_product": 16, "bad_primes": ["(w)", "(-w+1)", "(-2*w+1)", "(3)"], "Lvalue": {"__RealLiteral__": 0, "data": "4.7868997978382464906921047090734783638", "prec": 130}, "sha": 4, "torsion_primes": [2], "n_bad_primes": 4, "reducible_primes": [2], "semistable": false, "disc": "(1032192)", "normdisc": 1065420324864, "conductor_norm_factors": [2, 3, 7], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 2.6642974075950554, "cm_type": 0}