{"torsion_structure": [2, 2], "ainvs": "1,0;0,0;0,0;4,0;1,0", "cm": 0, "torsion_gens": ["[[-1/4,0],[1/8,0],[1,0]]", "[[0,-2],[0,1],[1,0]]"], "number": 1, "rank": 1, "field_label": "2.0.4.1", "galois_images": ["2Cs"], "conductor_norm": 4225, "abs_disc": 4, "iso_nlabel": 0, "rank_bounds": [1, 1], "conductor_ideal": "(65)", "base_change": ["65.a2", "1040.f2"], "local_data": [{"p": "(-w-2)", "cp": 2, "kod": 6, "red": -1, "normp": 5, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}, {"p": "(2*w+1)", "cp": 2, "kod": 6, "red": -1, "normp": 5, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}, {"p": "(-3*w-2)", "cp": 2, "kod": 6, "red": -1, "normp": 13, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}, {"p": "(2*w+3)", "cp": 2, "kod": 6, "red": -1, "normp": 13, "rootno": 1, "ord_cond": 1, "ord_disc": 2, "ord_den_j": 2}], "analytic_rank": 1, "minD": "(4225)", "label": "2.0.4.1-4225.5-a1", "jinv": "6967871/4225,0", "conductor_label": "4225.5", "class_deg": 4, "reg": {"__RealLiteral__": 0, "data": "0.18775704933063316090223643841228915883", "prec": 133}, "class_size": 4, "class_label": "2.0.4.1-4225.5-a", "iso_label": "a", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "4225.5-a1", "short_class_label": "4225.5-a", "isogeny_matrix": [[1, 2, 2, 2], [2, 1, 4, 4], [2, 4, 1, 4], [2, 4, 4, 1]], "torsion_order": 4, "equation": "{y}^2+{x}{y}={x}^{3}+4{x}+1", "gens": ["[[1,0],[2,0],[1,0]]"], "ngens": 1, "signature": [0, 1], "trace_hash": 1236043136808907351, "heights": [{"__RealLiteral__": 0, "data": "0.18775704933063316090223643841228915883", "prec": 133}], "isodeg": [1, 2], "omega": {"__RealLiteral__": 0, "data": "3.4215145161344667838159895156985877169", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 16, "bad_primes": ["(-w-2)", "(2*w+1)", "(-3*w-2)", "(2*w+3)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.2848269395826730601204719182874633143", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 4, "reducible_primes": [2], "semistable": true, "disc": "(-4225)", "normdisc": 17850625, "conductor_norm_factors": [5, 13], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 1.4408714212424685, "cm_type": 0}