Tate-Shafarevich groups of some constant elliptic curves.

The task of finding rational points on elliptic curves is fundamental to their study, and a general descent procedure involving the Kummer sequence is well documented. However, for general elliptic curves, this procedure is still computationally expensive. A recent work by Creutz and Voloch uses the isogeny volcano structure of some elliptic curves to provide more information about the Tate-Shafarevich groups. We aim to describe the key results of this paper, as well as provide explicit descriptions of low order torsion of the Tate-Shafarevich groups of these curves