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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
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