Finding an elliptic curve with CM by $\mathbb{Z}[\sqrt{-17}]$

1.4k Views Asked by At

I have the imaginary quadratic field $K= \mathbb{Q}(\sqrt{-17})$ with $\mathcal{O}_K = \mathbb{Z}[\sqrt{-17}]$. Now I want to have the $j$-Invariant of an elliptc curve $E$ with complex multiplication by $\mathcal{O}_K$. For a given elliptic curve I know how to compute the $j$-invariant with PARI. Therefore just a hint how to get this curve would be perfect!