On the rational cuspidal subgroup and the rational torsion points of J(0)(pq)

For two distinct prime numbers p, q, we compute the rational cuspidal subgroup C(pq) of J(0)(pq) and determine the e-primary part of the rational torsion subgroup of the old subvariety of Ja(pp) for most primes C. Some results of Berkovic on the nontriviality of the Mordell-Weil group of some Eisenstein factors of J(0)(pq) are also refined.