Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, on b=-1, c=-a-d. Specialization (a,b,c,d)=(-2,-1,-1,3), t=1249/393, w=36386126/154449 on w^2=D_{a,d}(t), where D_{a,d}(t)=L_{a,d}(t)^2-4(a^3+1)d^3(t-a)(t-d)^3 and the cubesum parameter k=(a^3+1)(t-a)w/8 up to rational cubic scaling, yields u^3+v^3=1511138090. PARI/GP 2.17.4 ellrank bounds [6,6].
Commentary
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