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We determine the index of five of the $7$ hypergeometric Calabi-Yau operatorsthat have finite index in $Sp_4(\mathbb{Z})$ and in two cases give a completedescription of the monodromy group. Furthermore we found six non-hypergeometricCalabi-Yau operators with finite index in $Sp_4(\mathbb{Z})$, most notably acase where the index is one.

Some monodromy groups of finite index in $Sp_4(\mathbb{Z})$