On Tate-Shafarevich Groups of some Elliptic Curves, by Franz Lemmermeyer
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. This is an update of preprint number 166.
Franz Lemmermeyer <email@example.com>