I want to verify Thm 5.6 in Silvermans Advanced Topics in the Arithmetic of Elliptic Curves that says $K(j(E),h(E[\mathbb{c}])$ is the ray class filed of $K$ modulo $\mathbb{c}$. I choose $K= \mathbb{Q}(i)$ and $\mathbb{c} = 2,3,4$. The $j$-invariant is in $\mathbb{Q}$ because its class number is $1$. And the Weberfunction is $h(x,y)= x^2$. I computed the torsion points and then we have $K(h(E[2])) = K$, $K(h(E[3])) = K(\sqrt{3})$ and $K(h(E[4])) = K(\sqrt{2})$.
Now I want to compute the ray class fields via an other method. I know something about PARI, but couldn't find there something. I am looking foreward for any ideas or help with some copmuter algebra (magma, sage, PARI). Thanks in advance!