A note on the hypergeometric datum $\big((\frac{1}{2},\frac{1}{6},\frac{5}{6}),(1,1)\big)$ and symmetric squares of elliptic curves

Abstract

This is an expository note on a mod $p$ congruence relating the truncated hypergeometric sums associated to $\big((\frac{1}{2},\frac{1}{6},\frac{5}{6}),(1,1)\big)$ to symmetric squares of elliptic curves.