{"torsion_structure": [], "ainvs": "0,0;1,1;0,0;-16342,3825;1561180,-365194", "cm": 0, "torsion_gens": [], "number": 4, "rank": 0, "field_label": "2.2.57.1", "galois_images": ["3B", "7B.6.1"], "conductor_norm": 256, "abs_disc": 57, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(16)", "base_change": [], "local_data": [{"p": "(w-4)", "cp": 4, "kod": -15, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 4, "ord_disc": 19, "ord_den_j": 7}, {"p": "(w+3)", "cp": 4, "kod": -29, "red": 0, "normp": 2, "rootno": -1, "ord_cond": 4, "ord_disc": 33, "ord_den_j": 21}], "analytic_rank": 0, "minD": "(1572864*w+66584576)", "label": "2.2.57.1-256.1-a4", "jinv": "-503450019/1048576,699691689/2097152", "conductor_label": "256.1", "class_deg": 21, "reg": 1, "class_size": 4, "class_label": "2.2.57.1-256.1-a", "iso_label": "a", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "256.1-a4", "short_class_label": "256.1-a", "isogeny_matrix": [[1, 3, 7, 21], [3, 1, 21, 7], [7, 21, 1, 3], [21, 7, 3, 1]], "torsion_order": 1, "equation": "{y}^2={x}^{3}+\\left(a+1\\right){x}^{2}+\\left(3825a-16342\\right){x}-365194a+1561180", "gens": [], "ngens": 0, "signature": [2, 0], "trace_hash": 287298652293280435, "heights": [], "isodeg": [1, 3, 7, 21], "omega": {"__RealLiteral__": 0, "data": "1.9155379375203222958241823315326228991", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 16, "bad_primes": ["(w-4)", "(w+3)"], "Lvalue": {"__RealLiteral__": 0, "data": "4.0595071670900881678429977241263958297", "prec": 130}, "sha": 1, "torsion_primes": [], "n_bad_primes": 2, "reducible_primes": [3, 7], "semistable": false, "disc": "(-1572864*w-66584576)", "normdisc": 4503599627370496, "conductor_norm_factors": [2], "nonmax_primes": [3, 7], "nonmax_rad": 21, "root_analytic_conductor": 2.6985841962667707, "cm_type": 0}