Let $A$ be an abelian variety over a field $k$, and let $N$ be a finite subgroup of $A$. Suppose that $N$ is also defined over $k$, or at least that all Galois automorphisms fixing $k$ leave $N$ invariant. Then I've heard it stated that there is an abelian variety $B / k$ and an isogeny $\phi: A \rightarrow B$ with kernel $N$, such that $\phi$ is defined over $k$. I can't seem to find this stated anywhere (except in Silverman, where it is stated for elliptic curves as an exercise) and am not sure how to prove it. Does anyone know how to prove this and/or where to cite it in the literature?