Torsion Points on Elliptic Curves in Weierstrass Form

Philipp Habegger

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arXiv · 1105.4435

Torsion Points on Elliptic Curves in Weierstrass Form

Philipp Habegger

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Abstract

We prove that there are only finitely many complex numbers $a$ and $b$ with $4a^3+27b^2\not=0$ such that the three points $(1,*),(2,*),$ and $(3,*)$ are simultaneously torsion on the elliptic curve defined in Weierstrass form by $y^2=x^3+ax+b$. This gives an affirmative answer to a question raised by Masser and Zannier. We thus confirm a special case in two dimensions of the relative Manin-Mumford Conjecture formulated by Pink and Masser-Zannier.

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Philipp Habegger. 2011-05-23. Torsion Points on Elliptic Curves in Weierstrass Form. https://arxiv.org/abs/1105.4435

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