51 citations · 217 across the 26 of their papers we have counts for
34 papers
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…
The density of integral quadratic forms having a -dimensional totally isotropic subspace
Lycka Drakengren, Tom Fisher
We investigate the probability that a random quadratic form in has a totally isotropic subspace of a given dimension. We show that this global probabili…
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…
Computing structure constants for rings of finite rank from minimal free resolutions
Tom Fisher, Lazar Radičević
We show how the minimal free resolution of a set of points in general position in projective space of dimension explicitly determines structure constants for a ring of ra…
On pairs of 17-congruent elliptic curves
Tom Fisher
We compute explicit equations for the surfaces Z(17,1) and Z(17,3) parametrising pairs of -congruent elliptic curves. We find that each is a double cover of the same elliptic K…
The density of polynomials of degree over having exactly roots in
Manjul Bhargava, John Cremona, Tom Fisher +1
We determine the probability that a random polynomial of degree over has exactly roots in , and show that it is given by a rational function of…