Suppose I have a hyperelliptic curve of genus $2$ over $\mathbb Q$. I want to get information about its Jacobian reduction at prime $p$ (especially, in case $p=2$). Also I'm interesting in the group of connected components of the Neron model of the Jacobian.

Is it possible to get such information using some computer algebra system (like Magma, Sage and etc)? I know that there is Sage (and Pari) function genus2reduction (Liu algorithms implementation) that is able to give information about almost all reductions. But it doesn't give enough information about reduction at $p=2$.

So I want to focus on case $p=2$ and I'm looking for other solution.

UPD Gave link at genus2reduction and pointed that it is implementation of Liu algorithms. Added after Victor Miller answer.