On the degree of the -torsion field of elliptic curves over \mathbb Q_\ell for \ell \not =p
Volume 195 / 2020
Acta Arithmetica 195 (2020), 13-55
MSC: Primary 11G05.
DOI: 10.4064/aa181029-8-11
Published online: 29 April 2020
Abstract
Let \ell and p \geq 3 be distinct prime numbers. Let E/\mathbb Q _{\ell } be an elliptic curve with p-torsion module E_p. Let \mathbb Q _{\ell }(E_p) be the p-torsion field of E. We provide a complete description of the degree of the extension \mathbb Q _{\ell }(E_p)/\mathbb Q _{\ell } in terms of standard information on E.
