{"torsion_structure": [2, 2], "ainvs": "1,1,0;1,-1,0;-5,0,1;140336236819129681,-67065389289594007,-44174316128285721;-26955350586605825705197871,12881712674525578166721139,8484866098384540422058642", "cm": 0, "torsion_gens": ["[[-182332383,87134959,57393646],[320740778,-153279049,-100961126],[1,0,0]]", "[[-423949109/4,202601357/4,133448511/4],[1491537217/8,-712791825/8,-469498383/8],[1,0,0]]"], "number": 5, "rank": 0, "field_label": "3.3.733.1", "galois_images": ["2Cs"], "conductor_norm": 2, "abs_disc": 733, "iso_nlabel": 2, "rank_bounds": [0, 0], "conductor_ideal": "(w^2-6)", "base_change": [], "local_data": [{"p": "(w^2-6)", "cp": 4, "kod": 8, "red": 1, "normp": 2, "rootno": -1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}], "analytic_rank": 0, "minD": "(w^2+w-8)", "label": "3.3.733.1-2.1-c5", "jinv": "10146617913/16,-266719409/16,-1494139287/16", "conductor_label": "2.1", "class_deg": 8, "reg": 1, "class_size": 6, "class_label": "3.3.733.1-2.1-c", "iso_label": "c", "degree": 3, "non_min_p": [], "q_curve": false, "short_label": "2.1-c5", "short_class_label": "2.1-c", "isogeny_matrix": [[1, 2, 4, 2, 2, 4], [2, 1, 8, 4, 4, 8], [4, 8, 1, 8, 2, 4], [2, 4, 8, 1, 4, 8], [2, 4, 2, 4, 1, 2], [4, 8, 4, 8, 2, 1]], "torsion_order": 4, "equation": "{y}^2+\\left(a+1\\right){x}{y}+\\left(a^{2}-5\\right){y}={x}^{3}+\\left(-a+1\\right){x}^{2}+\\left(-44174316128285721a^{2}-67065389289594007a+140336236819129681\\right){x}+8484866098384540422058642a^{2}+12881712674525578166721139a-26955350586605825705197871", "gens": [], "ngens": 0, "signature": [3, 0], "trace_hash": 1403466619067656722, "heights": [], "isodeg": [1, 2, 4], "omega": {"__RealLiteral__": 0, "data": "141.42489352022092802459644687142236142", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 4, "bad_primes": ["(w^2-6)"], "Lvalue": {"__RealLiteral__": 0, "data": "1.3059119072702768812076412045647371135", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2], "semistable": true, "disc": "(w^2+w-8)", "normdisc": 16, "conductor_norm_factors": [2], "nonmax_primes": [2], "nonmax_rad": 2, "root_analytic_conductor": 2.7155775319800473, "cm_type": 0}