2 citations · 2 across the 3 of their papers we have counts for
3 papers
math.NT2023
Minimisation of 2-coverings of genus 2 Jacobians
Tom Fisher, Mengzhen Liu
An important problem in computational arithmetic geometry is to find changes of coordinates to simplify a system of polynomial equations with rational coefficients. This is tackled…
math.NT2023★ 2 cited
Computing the Cassels-Tate pairing on the 2-Selmer group of a genus 2 Jacobian
Tom Fisher, Jiali Yan
We describe a method for computing the Cassels-Tate pairing on the 2-Selmer group of the Jacobian of a genus 2 curve. This can be used to improve the upper bound coming from 2-desc…
math.NT2022
On binary quartics and the Cassels-Tate pairing
Tom Fisher
We use the invariant theory of binary quartics to give a new formula for the Cassels-Tate pairing on the -Selmer group of an elliptic curve. Unlike earlier methods, our formula…