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.