Constructing Isogenies of Elliptic Curves Over Finite Fields
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It is known that two elliptic curves over a finite field are isogenous if and only if they have the same number of points over that field (theorem due to Tate). The proof of Tate’s theorem is, unfortunately, highly abstract and does not aid in constructing such an isogeny. This paper will outline and discuss the algorithm that Galbraith put forth to achieve this task.