{"torsion_structure": [], "ainvs": [0, 0, 1, -7, 6], "num_bad_primes": 1, "cm": 0, "lmfdb_number": 1, "number": 1, "rank": 3, "sha_primes": [], "sha": 1, "nonmax_rad": 1, "torsion": 1, "iso_nlabel": 0, "aplist": [-2, -3, -4, -4, -6, -4, -4, -7, -6, -6, -2, 0, 0, -8, -9, -9, -11, -2, -12, -8, -14, 9, -2, 11, 6], "bad_primes": [5077], "real_period": {"data": "4.15168798309", "prec": 44, "__RealLiteral__": 0}, "min_quad_twist": {"disc": 1, "label": "5077a1", "lmfdb_label": "5077.a1"}, "isogeny_matrix": [[1]], "local_data": [{"ord_disc": 1, "ord_cond": 1, "kod": "\\\\( I_{1} \\\\)", "ord_den_j": 1, "p": 5077, "cp": 1, "rootno": 1, "red": -1}], "conductor": 5077, "lmfdb_iso": "5077.a", "2adic_label": "X1", "label": "5077a1", "tor_gro": {"6:6:2093830264528:1": "2,2", "3:3:20308:1": "2"}, "jinv": "37933056/5077", "manin_constant": 1, "2adic_log_level": 0, "class_deg": 1, "nonmax_primes": [], "class_size": 1, "sha_an": {"data": "1.0", "prec": 10, "__RealLiteral__": 0}, "isogeny_degrees": [1], "torsion_generators": [], "degree": 1984, "iwp0": 0, "2adic_gens": [], "iwdata": {"11": [3, 0], "13": [3, 0], "17": [3, 0], "23": [3, 0], "19": [3, 0], "47": [3, 0], "31": [3, 0], "37": [3, 3, 0], "43": [3, 0], "29": [3, 0], "3": [3, 3, 0], "2": [4, 3, 0], "5": [3, 0], "7": [3, 0], "41": [3, 3, 0], "5077": "o?"}, "torsion_primes": [], "optimality": 1, "tor_degs": [3, 6], "signD": 1, "tamagawa_product": 1, "special_value": {"data": "1.73184990012", "prec": 44, "__RealLiteral__": 0}, "heights": [1.3685725053539302, 1.2050811041858522, 0.990906333153088], "modp_images": [], "num_int_pts": 36, "trace_hash": 129556073554127214, "equation": "\\( y^2 + y = x^{3} - 7 x + 6 \\)", "tor_fields": ["6.6.2093830264528.1", "3.3.20308.1"], "gens": ["(-2:3:1)", "(-1:3:1)", "(0:2:1)"], "regulator": {"data": "0.417143558758", "prec": 47, "__RealLiteral__": 0}, "semistable": true, "anlist": [0, 1, -2, -3, 2, -4, 6, -4, 0, 6, 8, -6, -6, -4, 8, 12, -4, -4, -12, -7, -8], "iso": "5077a", "2adic_index": 1, "xcoord_integral_points": [-3, -2, -1, 0, 1, 2, 3, 4, 8, 11, 14, 21, 37, 52, 93, 342, 406, 816], "lmfdb_label": "5077.a1"}