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

Author(s): Seng-Kiat Chua; San Ling
Journal: Proc. Amer. Math. Soc. 125 (1997), 2255-2263.
MSC (1991): Primary 11G18, 11F03, 11F20, 14H40
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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: 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
Copyright of article: Copyright 1997, American Mathematical Society

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