On the rational cuspidal subgroup and the rational torsion points of $J_0(pq)$
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 $\ell$-primary part of the rational torsion subgroup of the old subvariety of $J_0(pq)$ for most primes $\ell$. Some results of BerkoviÄ on the nontriviality of the Mordell-Weil group of some Eisenstein …