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Can someone explain to me on how to obtain the endomorphism for elliptic curve with CM by $(1+\sqrt{-11}) /2$?

Given the elliptic curve over $F_{p}$ as $y^2=x^3-13824/539 x + 27648/539 \dots$ how do we actually calculate it? Do we still need to use the Weierstrass $\wp$-function or is there any other method to solve this question?

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The usual method to do this is to use formulas due to Velu. There's an implementation in PARI given at http://perso.ens-lyon.fr/francois.brunault/parigp/velu.gp

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