{"torsion_structure": [2, 4], "ainvs": "1,1;0,-1;0,0;520,-520;-4225,0", "cm": 0, "torsion_gens": ["[[0,-65],[-520,65],[1,0]]", "[[0,10],[5,-10],[1,0]]"], "number": 5, "rank": 1, "field_label": "2.0.3.1", "galois_images": ["2Cs"], "conductor_norm": 12675, "abs_disc": 3, "iso_nlabel": 1, "rank_bounds": [1, 1], "conductor_ideal": "(-130*w+65)", "base_change": ["195.a4", "585.g4"], "local_data": [{"p": "(-2*w+1)", "cp": 8, "kod": 12, "red": 1, "normp": 3, "rootno": -1, "ord_cond": 1, "ord_disc": 8, "ord_den_j": 8}, {"p": "(-4*w+1)", "cp": 4, "kod": 8, "red": 1, "normp": 13, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}, {"p": "(4*w-3)", "cp": 4, "kod": 8, "red": 1, "normp": 13, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}, {"p": "(5)", "cp": 4, "kod": 8, "red": 1, "normp": 25, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}], "analytic_rank": 1, "minD": "(1445900625)", "label": "2.0.3.1-12675.2-b5", "jinv": "15551989015681/1445900625,0", "conductor_label": "12675.2", "class_deg": 16, "reg": {"__RealLiteral__": 0, "data": "0.346553450838422", "prec": 57}, "class_size": 8, "isogeny_degrees": [1, 2, 4], "class_label": "2.0.3.1-12675.2-b", "iso_label": "b", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "12675.2-b5", "short_class_label": "12675.2-b", "isogeny_matrix": [[1, 8, 16, 8, 4, 16, 2, 4], [8, 1, 8, 4, 2, 8, 4, 8], [16, 8, 1, 2, 4, 4, 8, 16], [8, 4, 2, 1, 2, 2, 4, 8], [4, 2, 4, 2, 1, 4, 2, 4], [16, 8, 4, 2, 4, 1, 8, 16], [2, 4, 8, 4, 2, 8, 1, 2], [4, 8, 16, 8, 4, 16, 2, 1]], "torsion_order": 8, "non-surjective_primes": [2], "equation": "{y}^2+\\left(a+1\\right){x}{y}={x}^{3}-a{x}^{2}+\\left(-520a+520\\right){x}-4225", "gens": ["[[-65,65],[-455,-65],[1,0]]"], "ngens": 1, "signature": [0, 1], "trace_hash": 110945280441189912, "heights": [{"__RealLiteral__": 0, "data": "0.346553450838422", "prec": 57}], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "0.370634167434087", "prec": 57}, "potential_good_reduction": false, "tamagawa_product": 512, "bad_primes": ["(-2*w+1)", "(-4*w+1)", "(4*w-3)", "(5)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.37303985147076", "prec": 54}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 4, "reducible_primes": [2], "semistable": true, "disc": "(1445900625)", "normdisc": 2090628617375390625}