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

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