I found in page 225 of this article(adsbygoogle = window.adsbygoogle || []).push({});

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:

[itex]End(E)\simeq \mathbb{Z}[\delta]=\mathbb{Z}+\delta\mathbb{Z}[/itex],

where

[itex]\delta=\frac{\sqrt{\Delta}}{2}[/itex] if [itex]\Delta [/itex] is even

[itex]\delta=\frac{1+\sqrt{\Delta}}{2}[/itex] if [itex]\Delta [/itex] 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

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# Endomorphism ring over an elliptic curve

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