show · ec.endomorphism all knowls · up · search:

An endomorphism of an elliptic curve defined over a field $K$ is an isogeny $\varphi:E\to E$ defined over the algebraic closure of $K$.

The set of all endomorphisms of $E$ forms a ring called the endomorphism ring of $E$, denoted $\End(E)$. The subring consisting of those endomorphisms defined over $K$ itself is denoted $\End_K(E)$.

$\End(E)$ always contains a subring isomorphic to $\Z$, since for $m\in\Z$ there is the multiplication-by-$m$ map $[m]:E\to E$.

Authors:
Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-06-18 02:40:26
Referred to by:
History: (expand/hide all)