For an elliptic curve $E$ defined over a field $K$, the Mordell-Weil group of $E/K$ is the group of $K$-rational points of $E$. It is denoted $E(K)$.
This is a special case of the Mordell-Weil group of an abelian variety.
The Mordell-Weil Theorem, first proved by Mordell for elliptic curves defined over $\Q$ and later generalized by Weil to abelian varieties $A$ over general number fields $K$, states that, if $K$ is a number field, then $A(K)$ is a finitely generated abelian group. Its rank is called the Mordell-Weil rank of $A$ over $K$.
- Review status: reviewed
- Last edited by David Roe on 2019-04-08 06:41:09