Source: cirosantilli/mordell-s-theorem
= Mordell's theorem
{c}
{title2=1922}
The <elliptic curve group> of all <elliptic curve over the rational numbers> is always a <finitely generated group>.
The number of points may be either finite or infinite. But when infinite, it is still a <finitely generated group>.
For this reason, the <rank of an elliptic curve over the rational numbers> is always defined.
TODO example.