Simultaneous Torsion in the Legendre Family

@article{Stoll2017SimultaneousTI,
title={Simultaneous Torsion in the Legendre Family},
author={Michael Stoll},
journal={Experimental Mathematics},
year={2017},
volume={26},
pages={446 - 459}
}
• M. Stoll
• Published 26 October 2014
• Mathematics
• Experimental Mathematics
ABSTRACT We improve a result due to Masser and Zannier, who showed that the set is finite, where Eλ: y2 = x(x − 1)(x − λ) is the Legendre family of elliptic curves. More generally, denote by T(α, β), for , α ≠ β, the set of such that all points with x-coordinate α or β are torsion on Eλ. By further results of Masser and Zannier, all these sets are finite. We present a fairly elementary argument showing that the set T(2, 3) in question is actually empty. More generally, we obtain an explicit…
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