The elliptic threefold y^2=x^3+16s^6+16t^6-32(t^3s^3+t^3+s^3)+16
  We present a method to calculate the rank of $E(\oQ(s,t))$ for the elliptic curve mentioned in the title. This method uses a generalization of a method from Van Geemen and Werner to calculate $h^4(Y)$ for nodal hypersurfaces $Y$. 
Remke Kloosterman