Endomorphism ring over an elliptic curve

[yavanna]

I found 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

 

[fresh_42]

See theorem 1 section 1.2 in http://math.uga.edu/~pete/SC1-endomorphisms.pdf
and for finite fields http://iml.univ-mrs.fr/~kohel/pub/thesis.pdf