Number Theory Seminar

David Zywina Cornell University
There are infinitely many elliptic curves over the rationals of rank 2

Friday, February 7, 2025 - 2:30pm
Malott 224

For an elliptic curve $E$ defined over $\mathbb{Q}$, the Mordell-Weil group $E(\mathbb{Q})$ is a finitely generated abelian group. We prove that there are infinitely many elliptic curves $E$ over $\mathbb{Q}$ for which $E(\mathbb{Q})$ has rank 2. Our elliptic curves will be given by explicit models and their ranks will be found using a $2$-descent. The infinitude of such elliptic curves will make use of a theorem of Tao and Ziegler.