$\GL_2$-type (reviewed)

A simple abelian variety $A$ is said to be of $\textbf{GL}_2$-type if the dimension of its endomorphism algebra $\mathrm{End}(A)\otimes\Q$ (as a $\Q$-vector space) is equal to the dimension of $A$ (as an abelian variety); a non-simple abelian variety is of $\textrm{GL}_2$-type if it is isogenous 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.