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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the rational cuspidal subgroup
and the rational torsion points of $J_0(pq)$


Authors: Seng-Kiat Chua and San Ling
Journal: Proc. Amer. Math. Soc. 125 (1997), 2255-2263
MSC (1991): Primary 11G18, 11F03, 11F20, 14H40
MathSciNet review: 1396972
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Abstract | References | Similar Articles | Additional Information

Abstract: 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 Berkovic on the nontriviality of the Mordell-Weil group of some Eisenstein factors of $J_0(pq)$ are also refined.


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Additional Information

Seng-Kiat Chua
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore
Email: matchua@nus.sg

San Ling
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore
Email: matlings@nus.sg

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03874-4
PII: S 0002-9939(97)03874-4
Received by editor(s): September 8, 1995
Received by editor(s) in revised form: March 10, 1996
Additional Notes: The authors would like to thanks Ken Ribet for private communication. We are also grateful to the referee for comments which helped improve the presentation of the paper.
Communicated by: William W. Adams
Article copyright: © Copyright 1997 American Mathematical Society