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On binary quartics and the Cassels-Tate pairing

Published 31 Aug 2022 in math.NT | (2208.14977v1)

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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Authors (1)

  1. Tom Fisher 

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