Are there any other integers a such that
$(5a^2-3)(a^2+1)$ is a perfect square
than $-7, -1, 1,7$ and if possible to find what are these integers. By checking on wolfram it says that they are the only one but i doubt wolfram is always correct in diophantines . I think that both terms in the product are of form $2x^2$ but after can't make much progress