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} }
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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