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Endomorphism ring over an elliptic curve

  1. Aug 23, 2011 #1
    I found in page 225 of this article

    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
     
    Last edited by a moderator: Apr 26, 2017
  2. jcsd
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