$\GL_2$-type (reviewed)

A simple abelian variety $A$ is said to be of $\textbf{GL}_2$-type if its endomorphism algebra $\mathrm{End}(A)\otimes\Q$ is commutative and has dimension (as a $\Q$-vector space) equal to the dimension of $A$ (as an abelian variety). More generally, an abelian variety is said to be of $\textbf{GL}_2$-type if it is isogenous (over the ground field) to a product of pairwise non-isogenous simple abelian varieties of $\textrm{GL}_2$-type.

A curve is said to be of $\text{GL}_2$-type if its Jacobian is of $\text{GL}_2$-type.