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

• Autores: S. Kamienny
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 147, Nº 2, 2009, págs. 285-293
• Idioma: inglés
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• Resumen

  • 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.