English

On binary quartics and the Cassels-Tate pairing

Number Theory 2022-09-01 v1

Abstract

We use the invariant theory of binary quartics to give a new formula for the Cassels-Tate pairing on the 22-Selmer group of an elliptic curve. Unlike earlier methods, our formula does not require us to solve any conics. An important role in our construction is played by a certain K3K3 surface defined by a (2,2,2)(2,2,2)-form.

Keywords

Cite

@article{arxiv.2208.14977,
  title  = {On binary quartics and the Cassels-Tate pairing},
  author = {Tom Fisher},
  journal= {arXiv preprint arXiv:2208.14977},
  year   = {2022}
}

Comments

15 pages, to appear in the proceedings of ANTS 2022

R2 v1 2026-06-28T00:30:14.678Z