{"torsion_structure": [2], "ainvs": "1,5,0,-5,-1,1;3,-5,-12,10,6,-3;-1,0,4,-3,-2,1;-8,-25,-9,13,3,-2;16,58,24,-50,-17,11", "cm": 0, "torsion_gens": ["[[1/2,13/4,5/2,-11/4,-3/2,3/4],[-5/4,-43/8,-21/8,29/4,15/8,-3/2],[1,0,0,0,0,0]]"], "number": 4, "rank": 1, "field_label": "6.6.434581.1", "galois_images": ["2B", "3B"], "conductor_norm": 71, "abs_disc": 434581, "iso_nlabel": 1, "rank_bounds": [1, 1], "conductor_ideal": "(w^3-3*w)", "base_change": [], "local_data": [{"p": "(w^3-3*w)", "cp": 6, "kod": 10, "red": 1, "normp": 71, "rootno": -1, "ord_cond": 1, "ord_disc": 6, "ord_den_j": 6}], "analytic_rank": 1, "minD": "(-84*w^5+193*w^4+266*w^3-449*w^2-207*w+102)", "label": "6.6.434581.1-71.2-b4", "jinv": "275925918956956389/128100283921,648706548947243049/128100283921,-856118405892448540/128100283921,-1637664927517631470/128100283921,556381569549059781/128100283921,761638833101910810/128100283921", "conductor_label": "71.2", "class_deg": 6, "reg": {"__RealLiteral__": 0, "data": "0.032661262933286870167621618797138607766", "prec": 137}, "class_size": 4, "class_label": "6.6.434581.1-71.2-b", "iso_label": "b", "degree": 6, "non_min_p": [], "q_curve": false, "short_label": "71.2-b4", "short_class_label": "71.2-b", "isogeny_matrix": [[1, 2, 6, 3], [2, 1, 3, 6], [6, 3, 1, 2], [3, 6, 2, 1]], "torsion_order": 2, "equation": "{y}^2+\\left(a^{5}-a^{4}-5a^{3}+5a+1\\right){x}{y}+\\left(a^{5}-2a^{4}-3a^{3}+4a^{2}-1\\right){y}={x}^{3}+\\left(-3a^{5}+6a^{4}+10a^{3}-12a^{2}-5a+3\\right){x}^{2}+\\left(-2a^{5}+3a^{4}+13a^{3}-9a^{2}-25a-8\\right){x}+11a^{5}-17a^{4}-50a^{3}+24a^{2}+58a+16", "gens": ["[[16,17,-12,-11,2,1],[-10,86,91,-95,-42,23],[1,0,0,0,0,0]]"], "ngens": 1, "signature": [6, 0], "trace_hash": 2146759119269473786, "heights": [{"__RealLiteral__": 0, "data": "0.032661262933286870167621618797138607766", "prec": 137}], "isodeg": [1, 2, 3, 6], "omega": {"__RealLiteral__": 0, "data": "5981.5737388344693552573314079832798313", "prec": 130}, "potential_good_reduction": false, "tamagawa_product": 6, "bad_primes": ["(w^3-3*w)"], "Lvalue": {"__RealLiteral__": 0, "data": "2.66720", "prec": 24}, "sha": 1, "torsion_primes": [2], "n_bad_primes": 1, "reducible_primes": [2, 3], "semistable": true, "disc": "(-18*w^5+5*w^4+110*w^3+7*w^2-49*w+71)", "normdisc": -128100283921, "conductor_norm_factors": [71], "nonmax_primes": [2, 3], "nonmax_rad": 6, "root_analytic_conductor": 84.03214510986909, "cm_type": 0}