{"torsion_structure": [4], "ainvs": "1,0;1,0;0,0;-146,0;621,0", "cm": 0, "torsion_gens": ["[[4,0],[-13,0],[1,0]]"], "number": 4, "rank": 1, "field_label": "2.0.4.1", "galois_images": ["2B"], "conductor_norm": 1089, "abs_disc": 4, "iso_nlabel": 0, "rank_bounds": [1, 1], "conductor_ideal": "(33)", "base_change": ["528.g1", "33.a1"], "local_data": [{"p": "(3)", "cp": 3, "kod": 7, "red": 1, "normp": 9, "rootno": -1, "ord_cond": 1, "ord_disc": 3, "ord_den_j": 3}, {"p": "(11)", "cp": 4, "kod": 8, "red": 1, "normp": 121, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}], "analytic_rank": 1, "minD": "(395307)", "label": "2.0.4.1-1089.1-a4", "jinv": "347873904937/395307,0", "conductor_label": "1089.1", "class_deg": 4, "reg": {"__RealLiteral__": 0, "data": "0.96638850749087193986529900023792014742", "prec": 133}, "class_size": 4, "class_label": "2.0.4.1-1089.1-a", "iso_label": "a", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "1089.1-a4", "short_class_label": "1089.1-a", "isogeny_matrix": [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], "torsion_order": 4, "equation": "{y}^2+{x}{y}={x}^{3}+{x}^{2}-146{x}+621", "gens": ["[[13/2,0],[-13/4,3/4],[1,0]]"], "ngens": 1, "signature": [0, 1], "trace_hash": 1684319434589811083, "heights": [{"__RealLiteral__": 0, "data": "0.96638850749087193986529900023792014742", "prec": 133}], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "1.0255859771174331474340959250924567027", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 12, "bad_primes": ["(3)", "(11)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.4866717525951256416611441035797139448", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 2, "reducible_primes": [2], "semistable": true, "disc": "(395307)", "normdisc": 156267624249, "conductor_norm_factors": [3, 11], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 1.0266573462849722, "cm_type": 0}