On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve
Daniel M. Kane
TL;DR
This paper investigates the distribution of 2-Selmer group ranks among twists of a specific elliptic curve, extending previous research to better understand their density and behavior.
Contribution
It generalizes Swinnerton-Dyer's work by analyzing the density of twists with specified 2-Selmer group ranks for a given elliptic curve.
Findings
Extended the density results for 2-Selmer groups of elliptic curve twists.
Provided new insights into the distribution patterns of Selmer ranks.
Enhanced understanding of the arithmetic properties of elliptic curves.
Abstract
We extend work of Swinnerton-Dyer on the density of the number of twists of a given elliptic curve that have 2-Selmer group of a particular rank.
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.