Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Endomorphism ring over an elliptic curve
  1. Elliptic Curves (Replies: 11)

  2. Elliptic curves (Replies: 1)

Loading...