  For primes p congruent to 1 mod 12, we present an explicit relation between
the traces of Frobenius on a family of elliptic curves with j-invariant 1728/t
and values of a particular 2F1-hypergeometric function over F_p. Additionally,
we determine a formula for traces of Hecke operators T_k(p) on spaces of cusp
forms of weight k and level 1 in terms of the same traces of Frobenius. This
leads to formulas for Ramanujan's tau-function in terms of hypergeometric
functions.
