{"torsion_structure": [10], "ainvs": "0,0,-3,0,1;-2,-4,4,1,-1;1,1,-3,0,1;-17,82,-46,-30,18;49,-205,93,76,-37", "cm": 0, "torsion_gens": ["[[0,9,-6,-3,2],[2,-15,13,5,-5],[1,0,0,0,0]]"], "number": 2, "rank": 0, "field_label": "5.5.14641.1", "galois_images": ["2B", "5B.1.1"], "conductor_norm": 23, "abs_disc": 14641, "iso_nlabel": 0, "rank_bounds": [0, 0], "conductor_ideal": "(-w^4+w^3+3*w^2-3*w-2)", "base_change": [], "local_data": [{"p": "(-w^4+w^3+3*w^2-3*w-2)", "cp": 10, "kod": 14, "red": 1, "normp": 23, "rootno": -1, "ord_cond": 1, "ord_disc": 10, "ord_den_j": 10}], "analytic_rank": 0, "minD": "(437*w^4-155*w^3-1436*w^2+599*w+478)", "label": "5.5.14641.1-23.3-a2", "jinv": "-9914142943608711568/41426511213649,34459978988291163906/41426511213649,13634528082311040086/41426511213649,-40938279688082030060/41426511213649,13485883457883008301/41426511213649", "conductor_label": "23.3", "class_deg": 10, "reg": 1, "class_size": 4, "class_label": "5.5.14641.1-23.3-a", "iso_label": "a", "degree": 5, "non_min_p": [], "q_curve": false, "short_label": "23.3-a2", "short_class_label": "23.3-a", "isogeny_matrix": [[1, 5, 10, 2], [5, 1, 2, 10], [10, 2, 1, 5], [2, 10, 5, 1]], "torsion_order": 10, "equation": "{y}^2+\\left(a^{4}-3a^{2}\\right){x}{y}+\\left(a^{4}-3a^{2}+a+1\\right){y}={x}^{3}+\\left(-a^{4}+a^{3}+4a^{2}-4a-2\\right){x}^{2}+\\left(18a^{4}-30a^{3}-46a^{2}+82a-17\\right){x}-37a^{4}+76a^{3}+93a^{2}-205a+49", "gens": [], "ngens": 0, "signature": [5, 0], "trace_hash": 1894256519342967484, "heights": [], "isodeg": [1, 2, 5, 10], "omega": {"__RealLiteral__": 0, "data": "993.12606699865359490731750704130415623", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 10, "bad_primes": ["(-w^4+w^3+3*w^2-3*w-2)"], "Lvalue": {"__RealLiteral__": 0, "data": "0.820765345", "prec": 37}, "sha": 1, "torsion_primes": [2, 5], "n_bad_primes": 1, "reducible_primes": [2, 5], "semistable": true, "disc": "(-205*w^4+125*w^3+686*w^2-398*w-838)", "normdisc": -41426511213649, "conductor_norm_factors": [23], "nonmax_primes": [2, 5], "nonmax_rad": 10, "root_analytic_conductor": 14.794377883723698, "cm_type": 0}