Special values of hypergeometric functions and periods of CM elliptic curves

Let $X_0^6(1)\mathrm{/}{W}_6$ be the Atkin-Lehner quotient of the Shimura curve $X_0^6(1)$ associated to a maximal order in an indefinite quaternion algebra of discriminant $6$ over $\mathbb{Q}$. By realizing modular forms on $X_0^6(1)\mathrm{/}{W}_6$ in two ways, one in terms of hypergeometric functions and the other in terms of Borcherds forms, and using Schofer’s formula for values of Borcherds forms at CM-points, we obtain special values of certain hypergeometric functions in terms of periods of elliptic curves over \overline\mathbb Q with complex multiplication.