Given the equation
$$ t^3=3a^2-3a+13 $$
I want to find integer solutions. WolframAlpha says $t=7,a=-10$ and $t=7,a=11$ are solutions, but how did it compute that?
I thought I wanted to find the intersection of $3a^2-3a+13$ and $t^3$, which gives $\approx 3.289$, but I'm not sure how to turn that into an integer.
I thought maybe solve for $a$, but I'm not sure how that helps me either
$$ a=\frac{3 \pm \sqrt{9-12(13-t^3)}}{6} $$