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The $\varepsilon$-form of a system of differential equations for Feynmanintegrals has led to tremendeous progress in our abilities to compute Feynmanintegrals, as long as they fall into the class of multiple polylogarithms. Itis therefore of current interest, if these methods extend beyond the case ofmultiple polylogarithms. In this talk I discuss Feynman integrals, which areassociated to elliptic curves and their differential equations. I show fornon-trivial examples how the system of differential equations can be broughtinto an $\varepsilon$-form. Single-scale and multi-scale cases are discussed.

Simple differential equations for Feynman integrals associated to elliptic curves