# Abelian groups in Elliptic curves [closed]

Do every elliptic curve defined over a prime field forms an abelian group?

• I'm voting to close this question as off-topic because it is about general mathematics. – fkraiem Apr 5 '17 at 7:21

This is a consequence to the Riemann-Roch theorem, which implies that the canonical map $E\to \mathrm{Pic}^0(E)$ is a bijection, and the latter is an abelian group by construction.