Simultaneous torsion in the Legendre family

Michael Stoll

We improve a result due to Masser and Zannier, who showed that the set $$\{\lambda \in \mathbb{C}\setminus \{0,1\}:(2,\sqrt{2(2-\lambda )}),(3,\sqrt{6(3-\lambda )})\in (E_{\lambda }{)}_{\text{tors}}\}$$ i…