Hypergeometric functions over $\mathbb{F}_q$ and traces of Frobenius for   elliptic curves
  We present here explicit relations between the traces of Frobenius endomorphisms of certain families of elliptic curves and special values of ${_{2}}F_1$-hypergeometric functions over $\mathbb{F}_q$ for $q \equiv 1 (\text{mod} 6)$ and $q \equiv 1 (\text{mod} 4)$. 
Rupam Barman and Gautam Kalita
math.NT