I was wondering what people would normally mean by a simple abelian variety $A$ where $A$ is defined over a field $k$ that is not algebraically closed.

The definition I found in for example on the bottom of page 29 in Langs book Abelian Varieties states:

An abelian variety $A$ is simple if $0$ and $A$ are the only abelian subvarieties of A.

But this definition is not entirely unambiguous for me. And other sources that I read only define being simple over algebraically closed fields.

My main question is: Would $A$ still be called simple if $A$ contains a nontrivial subvariety $B$ that is defined over $\bar k$ but such that $0$ and $A$ are the only subvarieties that are defined over $k$?

The reason I am asking is because I want to apply the results of http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.6978 to the weil restriction of an elliptic curve $A=Res_{K/\mathbb Q}E$. One of the hypothesis of that article is that $A$ must be simple. But depending on the definition of simple it might be so that $Res_{K/\mathbb Q}E$ is never simple as variety over $\mathbb Q$