= Rank of an elliptic curve over the rational numbers
{tag=Rank of a group}
{title2=$r$}
{wiki=Rank_of_an_elliptic_curve}
= Rank of the elliptic curve over the rational numbers
{synonym}
<Mordell's theorem> guarantees that <rank of a group>[the rank] (number of elements in the <generating set of the group>) is always well defined for an <elliptic curve over the rational numbers>. But as of 2023 there is no known algorithm which calculates the rank of any curve!
TODO list of known values and algorithms? The <Birch and Swinnerton-Dyer conjecture> would immediately provide a stupid algorithm for it.