In this talk, we discuss the cuspidal group of J0(pq) and the rational torsion points of J0(pq).
We prove the following statement. If a prime ell does not divide 6pq*gcd(p-1, q-1)*gcd(p-1,q+1)*(q-1,p+1), then the ell-primary part of the rational torsion subgroup of J0(pq) is isomorphic to the ell-primary subgroup of the cuspidal group.