Tom Fisher's Home Page


My research interests are in arithmetical algebraic geometry and computational number theory. In particular I work on elliptic curve descent calculations, and the construction of explicit elements in the Tate-Shafarevich group.

I am compiling a list of genus one curves that are counter-examples to the Hasse principle and have Jacobian of small conductor. The list so far covers elements of Sha of order 3 and order 5.

The PhD theses of my students Mohammad Sadek, Graham Sills, Monique van Beek, Zexiang Chen, Lazar Radičević and Jiali Yan are available by following these links.

Publications and Preprints

PhD Thesis    On 5 and 7 descents for elliptic curves

Last updated 22nd January 2024