Our main interest lies in exploring isomorphisms of elliptic curves. In particular, we focus on two curves defined over a base field and look at which extension fields the curves are isomorphic over. Elliptic curves have a fascinating structure behind them. This structure allows for much to be explored and studied.
Niemerg, Mathew, "Isomorphisms of Elliptic Curves over Extensions of Finite Fields" (2007). Mathematical Sciences Technical Reports (MSTR). 45.