Learning Seminar on Elliptic Curves

Nicolas Banks, Department of Pure Mathematics, University of Waterloo

"Dual Isogenies, the Weil Pairing, and the Structure of Endomorphism Rings"

We conclude our review of the geometry of elliptic curves by studying dual isogenies. This allows us to prove important results on torsion elements on elliptic curves, culminating in the construction of the Weil pairing and the algebraic structure of rings of isogenies.