Shafarevich-Tate Groups of Nonsquare Order

Abstract of the paper: We prove that for all p<25000 there is an abelian variety with Sha of order p x (perfect square)

LaTeX (the latex file also requires this class file)

I gave a talk at the Lenstra Treuerfeest on nonsquare Shafarevich-Tate groups, and here are my slides (585KB PDF).
Here are the slides from my August 2003 talk at Microsoft Research about nonsquare Shafarevich-Tate Groups (1.6MB PDF).