In this talk, we discuss the cuspidal group of $$extract_itex$$J_0(pq)$$/extract_itex$$ and the rational torsion points of $$extract_itex$$J_0(pq)$$/extract_itex$$.
We prove the following statement. If a prime $$extract_itex$$ell$$/extract_itex$$ does not divide 6pq*gcd(p-1, q-1)*gcd(p-1,q+1)*(q-1,p+1), then the $$extract_itex$$ell$$/extract_itex$$-primary part of the rational torsion subgroup of $$extract_itex$$J_0(pq)$$/extract_itex$$ is isomorphic to the $$extract_itex$$ell$$/extract_itex$$-primary subgroup of the cuspidal group.