Evaluating $j$-invariant in PARI/GP.

Question

Is there any command to evaluate $j$-invariant in PARI/GP?

In Pari/Gp reference card there is $\operatorname{ellj}(x)$ function; but I am not understanding how to evaluate $j(i)$ or $j(\sqrt{-2})$.

Any hint is also welcome; Thanks

Answer 1

Exactly what it says on the tin. One evaluates $j(x+iy)$ with the command ellj(x+I*y). Sample:

This gives $j(i)=1728$, $j(\sqrt{-2})=8000$, $j(e^{\frac 23 \pi i}) = 0$.