when I Find the diophantine-equation rational points $$2y^2=x^6-x^2+2$$

I using Faltings's theorem showed that there are only finitely many solutions,if we assmue that $(x_{i},y_{i}),i=1,2,\cdots,N$ is solution,and $x_{i}=\dfrac{p_{i}}{q_{i}},i=1,2,\cdots,N$,can we estimate upper bound of $|p_{i}|$ or $|q_{i}|?$