Order of real component group of J0(N)

William Stein
  1. Table for all N < 1598, and the code to make it.
  2. Table for N=pq, where p,q are prime, and the code to make it.

A Conjecture About the Data

Conjecture (Frank Calegari)

Let m = #odd prime factors of N + {1, if N = 0 mod 8
                                   {0, otherwise.

Then the component group is isomorphic to (Z/2Z)^f, where
f = 2^m - 1.