On binary quartics and the Cassels-Tate pairing

2022/08/31 by Fisher, Tom · 1 citation
#11G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2208.14977

Abstract

We use the invariant theory of binary quartics to give a new formula for the Cassels-Tate pairing on the 2-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 K3 surface defined by a (2,2,2)-form.

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