By enter link description here an elliptic curve is $F$-pure if and only if the $F$-pure threshold of its defining ideal is $1$. Whether there exists an $F$-pure local ring $R=A/\mathfrak{a}$ such that $\text{fpt}(\mathfrak{a})\neq 1$?

According to this reference an elliptic curve is $F$-pure if and only if the $F$-pure threshold of its defining ideal is $1$. Does there exist an $F$-pure local ring $R=A/\mathfrak{a}$ such that $\text{fpt}(\mathfrak{a})\neq 1$?