Complete solutions of a family of cubic Thue equations (Q2433591)

For \(n>1\), the only solutions to the parametrized family of Thue equations \[ x^3+(n^8+2n^6-3n^5+3n^4-4n^3+5n^2-3n+3)x^2y-(n^3-2)n^2xy^2-y^3=\pm 1 \] are \(\pm \{(1,0), (0,1)\}\). This is proved using Baker's method. There are a few listed extra solutions for \(n=0,1\).