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In a 1998 paper, Kaneko and Zagier explain unpublished work of Atkin which exhibits an infinite sequence of polynomials with the property that when suitable polynomials are reduced mod p for a prime p, one gets the locus of supersingular elliptic curves. Here we generalize this phenomenon by considering the continued fraction expansions of modular and quasimodular forms.

Generalization of Atkin’s orthogonal polynomials and supersingular elliptic curves