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

Abstract

AbstractWe carry out an Eisenstein prime descent to prove the finiteness of the Mordell-Weil group of the Eisenstein quotients ofJ1(p) for certain values ofpthat 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.