The **endomorphism ring** $\End(E)$ of an elliptic curve \(E\) is the ring of all endomorphisms of \(E\) defined over $K$. For endomorphisms defined over extensions, we speak of the geometric endomorphism ring of $E$.

For elliptic curves defined over $\Q$, this ring is always isomorphic to \(\Z\) consisting of the multiplication-by-$m$ maps $[m] \colon E\to E$ for $m \in \Z$.

This is a special case of the endomorphism ring of an abelian variety.

**Knowl status:**

- Review status: reviewed
- Last edited by John Voight on 2020-09-26 16:59:43

**Referred to by:**

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**History:**(expand/hide all)

- 2020-09-26 16:59:43 by John Voight (Reviewed)
- 2018-06-18 04:35:54 by John Jones (Reviewed)

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