Open in CoCalc
William A. Stein
The odd part of the intersection graph of J_0(N).
The odd part of the intersection graph of J
list of pairs [N,k] to obtain the odd intersection graph for weight-k modular symbols of level N. You can also enter a single integer, in which case the weight k is automatically set equal to 1. When k=2, the intersection graph is obtained as follows. Let A
, ..., A
be the abelian subvarieties of J
(N) corresponding to newform classes of some level dividing N. This list is ordered so that ... The numbers in the list correspond to the
newforms of level N
. For example, if you enter "389" for N you will obtain the list [0,0,0,0,25]. Then by consulting
the newform table
you can see that 25 is an upper bound on the odd part of the analytic order of Sha for the 20-dimensional abelian variety
I have computed this number for many square-free integers N up to 2500. I have not computed the number for non-square-free N, because I'm not sure how to compute the c
, so the upper bound I get (with c
= 1) is not very exciting. Click the "List known levels" button below to see exactly what I've computed.