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• For my number theory seminar with Scott Carnahan I wrote a paper describing an important corollary of the Eichler-Shimura relation in the theory of modular forms. The actual relation is somewhat difficult to state, but the important corollary relates the number of points on certain elliptic curves $E$ over finite fields to the Fourier coefficients of certain modular forms of weight $2$. You can find the paper here. Although the class is over, corrections and comments are of course welcome. (Though I hope Scott doesn’t change my grade if someone spots a mistake he missed!)