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](http://www.sagemath.org/doc/reference/plane_curves/sage/interfaces/genus2reduction.html) (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.


***UPD2*** Thanks to **Michael Stoll**. There is an [answer](https://mathoverflow.net/a/171767/10300) for almost all cases. But for some curves his solution still doesn't work. So I'm still looking for something else. For example it is impossible to get information about reduction at $p=2$ for such curves like $y^2 = 16\*x^6 + 32\*x^5 + 16\*x^4 + 32\*x^3 + 96\*x^2 + 64\*x + 16$.



Calculate reduction of Jacobian of hyperelliptic curve
The relevant information can be obtained from a regular model of the curve over ${\mathbb Z}\_p$. Such a model can be computed by repeatedly blowing up points or components of the special fiber that are singular on the arithmetic surface one obtains from the original curve. More or less detailed examples of this can be found in various places, for example [here](http://www.mathe2.uni-bayreuth.de/stoll/schrift.html#AG17) or [here](http://www.mathe2.uni-bayreuth.de/stoll/schrift.html#AG9). The component group can be obtained from the intersection matrix of the resulting special fiber.


There is an implementation of regular models in Magma by Steve Donnelly that can do this computations in many (but not yet all) cases. See the function "RegularModel" and the documentation [here](http://magma.maths.usyd.edu.au/magma/handbook/text/1322#14511).


