On Tate-Shafarevich Groups of some Elliptic Curves, by Franz Lemmermeyer

Preprint number 176 is an update of this preprint. Hence this version has been removed. Generalizing results of Stroeker and Top we show that the $2$-ranks of the Tate-Shafarevich groups of the elliptic curves $y^2 = (x+k)(x^2+k^2)$ can become arbitrarily large. We also present a conjecture on the rank of the Selmer groups attached to rational $2$-isogenies of elliptic curves.

Franz Lemmermeyer <lemmerm@mpim-bonn.mpg.de>