Distribution of Mordell--Weil ranks of families of elliptic curves
Bartosz Naskr\k{e}cki

TL;DR
This paper investigates the distribution of Mordell--Weil ranks in a family of elliptic curves parametrized by coprime polynomials related to the Pythagorean conic, completing previous partial results with general proofs.
Contribution
It provides the complete characterization of Mordell--Weil rank distribution for a broad family of elliptic curves, extending earlier special case analyses.
Findings
Distribution patterns of ranks established
General results proved for the family of curves
Completes previous partial analyses
Abstract
We discuss the distribution of Mordell--Weil ranks of the family of elliptic curves where are coprime polynomials that parametrize the projective smooth conic and are elements from . In our previous papers we discussed certain special cases of this problem and in this article we complete the picture by proving the general results.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
