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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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    $\begingroup$ I think this is a perfectly fine question. Please do not vote to close it. $\endgroup$
    – GH from MO
    Commented Aug 16, 2016 at 17:33
  • $\begingroup$ Related question: mathoverflow.net/questions/153730/… $\endgroup$
    – Watson
    Commented May 7, 2021 at 19:01

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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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