On Mon, Jun 27, 2016 at 2:28 PM, Sam Bloom <cincodemayo5...@gmail.com> wrote: > Hello, > > I would like to use Sage to study the reduction at a prime of a modular > abelian variety A over a number field (or at least over QQ). By "modular" I > mean either J0(N), for N a positive integer, or the abelian variety > associated to a particular newform of level N and weight 2. > > Is there any functionality for doing this? I would like to have, for > instance, the p-rank, Frobenius polynomial, zeta function, and so on. >
If p is good: It is possible to compute the charpoly of Frobenius in terms of the charpoly of T_p -- see page 8 (sec 3.5) of http://wstein.org/papers/shacomp/ to understand why/how. I don't know of anything Sage can compute about A/F_p that isn't a direct consequence of knowing the charpoly of Frob... If p is multiplicative, Sage can compute the order of the component group of the special fiber of the Neron model of A at p. > Thanks, > Sam > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- William (http://wstein.org) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
