51 citations · 217 across the 26 of their papers we have counts for
4 papers · 1 filter
The proportion of plane cubic curves over that everywhere locally have a point
Manjul Bhargava, John Cremona, Tom Fisher
We show that the proportion of plane cubic curves over that have a -rational point is a rational function in , where the rational function is inde…
What is the probability that a random integral quadratic form in variables is isotropic?
Manjul Bhargava, John Cremona, Tom Fisher
We show that the density of quadratic forms in variables over that are isotropic is a rational function in , where the rational function is independent of $p…
Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve
Tom Fisher, Rachel Newton
We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modific…
Invariant theory for the elliptic normal quintic, II. The covering map
Tom Fisher
A genus one curve C of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We prove a result characterising the covariants for these mo…