# Endomorphism ring over an elliptic curve

1. Aug 23, 2011

### yavanna

http://www.dm.unito.it/~cerruti/ac/schoof-counting.pdf"

that the endomorphism group over an elliptic curve is isomorphic to a complex quadratic order:

$End(E)\simeq \mathbb{Z}[\delta]=\mathbb{Z}+\delta\mathbb{Z}$,
where
$\delta=\frac{\sqrt{\Delta}}{2}$ if $\Delta$ is even
$\delta=\frac{1+\sqrt{\Delta}}{2}$ if $\Delta$ is odd

Does anyone know where I can find some info and a rigorous definition of a complex quadratic order, and the proof of that result?
Thanks

Last edited by a moderator: Apr 26, 2017