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I have a supersingular elliptic curve $E$ with a known endomorphism ring $\operatorname{End}(E)$. I'd like to find an isogeny $\varphi: E \rightarrow E'$, and by Deuring correspondence I know the corresponding ideal $I_{\varphi}$ in quaternion algebra. How could I find the endomorphism ring of $E'$ in this case?

tuner007
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    If you already have the ideal I for the isogeny, the endomorphism ring of E' should just be the right order of I. Magma has a built in function RightOrder(I) to perform this calculation. – djao Dec 23 '24 at 18:17

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