On binary quartics and the Cassels-Tate pairing


Type
Article
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Authors
Fisher, Tom 
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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Keywords
Journal Title
Research in Number Theory
Conference Name
Journal ISSN
2363-9555
Volume Title
Publisher
Springer