On the rational cuspidal subgroup and the rational torsion points of J0(pq)

Abstract

For two distinct prime numbers p, q, we compute the rational cuspidal subgroup C(pq) of J0(pq) and determine the l-primary part of the rational torsion subgroup of the old subvariety of J0(pq) for most primes l. Some results of Berkovic on the nontriviality of the Mordell-Weil group of some Eisenstein factors of J0(pq) are also refined. © 1997 American Mathematical Society.