Highly Influenced

# A Heuristic for Boundedness of Ranks of Elliptic Curves

@inproceedings{Park2016AHF, title={A Heuristic for Boundedness of Ranks of Elliptic Curves}, author={Jennifer Park and Bjorn Poonen and John Voight and Melanie Matchett Wood}, year={2016} }

- Published 2016

We present a heuristic that suggests that ranks of elliptic curves E over Q are bounded. In fact, it suggests that there are only finitely many E of rank greater than 21. Our heuristic is based on modeling the ranks and Shafarevich–Tate groups of elliptic curves simultaneously, and relies on a theorem counting alternating integer matrices of specified rank. We also discuss analogues for elliptic curves over other global fields.