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Some remarks on a theorem of Parent and generalizing Ogg's conjecture

Published online by Cambridge University Press:  01 September 2009

S. KAMIENNY
S. KAMIENNY*
Affiliation:
Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., Los Angeles, CA 90089-2532, U.S.A. e-mail: [email protected]
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Abstract

We carry out an Eisenstein prime descent to prove the finiteness of the Mordell-Weil group of the Eisenstein quotients of J1(p) for certain values of p that are relevant to torsion in elliptic curves over cubic fields. We then use this to recover some results of Parent. Our methods suggest a possible generalization of Ogg's conjecture for torsion in elliptic curves over number fields.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 285 - 293
Copyright
Copyright © Cambridge Philosophical Society 2009

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