{"torsion_structure": [4], "ainvs": "0,1;1,0;0,1;-23,-15;46,31", "cm": -64, "torsion_gens": ["[[2,1],[-2,-1],[1,0]]"], "number": 8, "rank": 0, "field_label": "2.2.8.1", "galois_images": [], "conductor_norm": 32, "abs_disc": 8, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(4*w)", "base_change": [], "local_data": [{"p": "(w)", "cp": 1, "kod": -1, "red": 0, "normp": 2, "rootno": 1, "ord_cond": 5, "ord_disc": 9, "ord_den_j": 0}], "analytic_rank": 0, "minD": "(16*w)", "label": "2.2.8.1-32.1-a8", "jinv": "41113158120,29071392966", "conductor_label": "32.1", "class_deg": 16, "reg": 1, "class_size": 8, "class_label": "2.2.8.1-32.1-a", "iso_label": "a", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "32.1-a8", "short_class_label": "32.1-a", "isogeny_matrix": [[1, 16, 8, 4, 2, 8, 4, 16], [16, 1, 8, 4, 8, 2, 16, 4], [8, 8, 1, 2, 4, 4, 8, 8], [4, 4, 2, 1, 2, 2, 4, 4], [2, 8, 4, 2, 1, 4, 2, 8], [8, 2, 4, 2, 4, 1, 8, 2], [4, 16, 8, 4, 2, 8, 1, 16], [16, 4, 8, 4, 8, 2, 16, 1]], "torsion_order": 4, "equation": "{y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\\left(-15a-23\\right){x}+31a+46", "gens": [], "ngens": 0, "signature": [2, 0], "trace_hash": 1924465176503130397, "heights": [], "isodeg": [1, 2, 4, 8, 16], "omega": {"__RealLiteral__": 0, "data": "27.500743272081491309960383119242228792", "prec": 130}, "potential_good_reduction": true, "tamagawa_product": 1, "bad_primes": ["(w)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.60768631422997331457673556779317068365", "prec": 133}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2], "semistable": false, "disc": "(16*w)", "normdisc": -512, "conductor_norm_factors": [2], "nonmax_primes": [], "nonmax_rad": 1, "root_analytic_conductor": 0.6011336530241873, "cm_type": -1}