While studying the location of the zeros of the Eisenstein series Ek(z), Rankin considered the determinants Δn of an associated Hankel matrix. He observed that the first few possess remarkable factorizations, and expressed the hope that a general theorem explaining these factorizations could be found. In this note we provide such a theorem by giving an explicit formula for Δn using work of Kaneko and Zagier on Atkin polynomials.