Division fields of elliptic curves with minimal ramification
Alvaro Lozano-RobledoUniversity of Connecticut, Storrs, USA
Let be an elliptic curve defined over , let be a prime number, and let . It is well-known that the -th division field of the elliptic curve contains all the -th roots of unity. It follows that the Galois extension is ramified above , and the ramification index of any prime of lying above is divisible by . The goal of this article is to construct elliptic curves such that is precisely , and such that the Galois group of is as large as possible, i.e., isomorphic to .
Cite this article
Alvaro Lozano-Robledo, Division fields of elliptic curves with minimal ramification. Rev. Mat. Iberoam. 31 (2015), no. 4, pp. 1311–1332DOI 10.4171/RMI/870