Dear all,

once again my question is all about $SL_2(\mathbb{Z})$ and $SL_2(\mathbb{Q})$ ! Which elements in $M \in SL_2(\mathbb{Q})$ can you write in the following form:

$M= NBN^{-1}$

with $N \in GL_2(\mathbb{Q})$ and $B \in SL_2(\mathbb{Z})$?

I guess that it is all of $SL_2(\mathbb{Q})$, but I do not know any proof for this fact!

Thank you very much again! Karl