Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, on the plane b=-1, c=-a-d. Specialization (a,b,c,d)=(20,-1,-18,-2), t=-76/129, w=16676660/16641 on w²=D_{a,d}(t), where k=(a³+1)(t-a)w/8 up to rational cubic scaling, gives the cubesum curve u³+v³=16143857730. PARI/GP 2.17.4 ellrank bounds [6,6].
jesper-petersen ·