Computing "isogeny graphs" using CM lattices

We describe a method to compute isogenies between polarized CM lattices.  
Using this we can compute the graph structure of (l,l)-isogeny graphs of 
abelian surfaces over finite fields.  We stress the words "graph structure" 
here, for we cannot determine absolute invariants of these objects in 
characteristic p (in characteristic 0 we can find complex value approximations).  
One positive aspect of this approach though is that computing endomorphism 
rings requires very little effort.  Some generalizations will be discussed 
and some examples provided.