{"torsion_structure": [2], "ainvs": "0,1;1,0;0,0;418,4360;146930,97280", "cm": 0, "torsion_gens": ["[[-73/2,16],[16,73/4],[1,0]]"], "number": 4, "rank": 1, "field_label": "2.0.8.1", "galois_images": ["2B", "3B"], "conductor_norm": 41616, "abs_disc": 8, "iso_nlabel": 4, "rank_bounds": [1, 1], "conductor_ideal": "(204)", "base_change": [], "local_data": [{"p": "(w)", "cp": 2, "kod": -11, "red": 0, "normp": 2, "rootno": 1, "ord_cond": 4, "ord_disc": 15, "ord_den_j": 3}, {"p": "(-w-1)", "cp": 2, "kod": 28, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 24, "ord_den_j": 24}, {"p": "(w-1)", "cp": 2, "kod": 10, "red": -1, "normp": 3, "rootno": 1, "ord_cond": 1, "ord_disc": 6, "ord_den_j": 6}, {"p": "(-2*w+3)", "cp": 1, "kod": 5, "red": -1, "normp": 17, "rootno": 1, "ord_cond": 1, "ord_disc": 1, "ord_den_j": 1}, {"p": "(2*w+3)", "cp": 2, "kod": 8, "red": -1, "normp": 17, "rootno": 1, "ord_cond": 1, "ord_disc": 4, "ord_den_j": 4}], "analytic_rank": 1, "minD": "(1788724321920*w-1783310266368)", "label": "2.0.8.1-41616.5-e4", "jinv": "-136155893118005119000/23588797316429601,410311536960329978125/94355189265718404", "conductor_label": "41616.5", "class_deg": 12, "reg": {"__RealLiteral__": 0, "data": "6.2931539160546365928133690826298624375", "prec": 130}, "class_size": 8, "class_label": "2.0.8.1-41616.5-e", "iso_label": "e", "degree": 2, "non_min_p": [], "q_curve": true, "short_label": "41616.5-e4", "short_class_label": "41616.5-e", "isogeny_matrix": [[1, 4, 3, 12, 6, 2, 4, 12], [4, 1, 12, 3, 6, 2, 4, 12], [3, 12, 1, 4, 2, 6, 12, 4], [12, 3, 4, 1, 2, 6, 12, 4], [6, 6, 2, 2, 1, 3, 6, 2], [2, 2, 6, 6, 3, 1, 2, 6], [4, 4, 12, 12, 6, 2, 1, 3], [12, 12, 4, 4, 2, 6, 3, 1]], "torsion_order": 2, "equation": "{y}^2+a{x}{y}={x}^{3}+{x}^{2}+\\left(4360a+418\\right){x}+97280a+146930", "gens": ["[[206367/1444,-2400/361],[-98076265/54872,-8695501/54872],[1,0]]"], "ngens": 1, "signature": [0, 1], "trace_hash": 1177362993633908278, "heights": [{"__RealLiteral__": 0, "data": "6.2931539160546365928133690826298624375", "prec": 130}], "isodeg": [1, 2, 3, 4, 6, 12], "omega": {"__RealLiteral__": 0, "data": "0.10396698373033479410080824502871436571", "prec": 133}, "potential_good_reduction": false, "tamagawa_product": 16, "bad_primes": ["(w)", "(-w-1)", "(w-1)", "(-2*w+3)", "(2*w+3)"], "Lvalue": {"__RealLiteral__": 0, "data": "3.7011679039764952941272628899277629300", "prec": 130}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 5, "reducible_primes": [2, 3], "semistable": false, "disc": "(-1788724321920*w+1783310266368)", "normdisc": 9579264905789834696884224, "conductor_norm_factors": [2, 3, 17], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 3.6099287541270066, "cm_type": 0}