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Author: William A. Stein
The odd part of the intersection graph of J_0(N).

# The odd part of the intersection graph of J0(N).

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Enter a semicolon-separated 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 A1, A2, ..., An be the abelian subvarieties of J0(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 389E.
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 cp, so the upper bound I get (with cp = 1) is not very exciting. Click the "List known levels" button below to see exactly what I've computed.

Output format:           HUMAN                MAGMA