Vol. 305, No. 1, 2020

 Recent Issues Vol. 305: 1 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Vol. 299: 1  2 Vol. 298: 1  2 Online Archive Volume: Issue:
 The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals
Torsion points and Galois representations on CM elliptic curves

Abbey Bourdon and Pete L. Clark

Vol. 305 (2020), No. 1, 43–88
Abstract

We prove several results on torsion points and Galois representations for complex multiplication (CM) elliptic curves over a number field containing the CM field. One result computes the degree in which such an elliptic curve has a rational point of order $N$, refining results of Silverberg (Compositio Math.68:3 (1988), 241–249; Contemp. Math. 133 (1992)). Another result bounds the size of the torsion subgroup of an elliptic curve with CM by a nonmaximal order in terms of the torsion subgroup of an elliptic curve with CM by the maximal order. Our techniques also yield a complete classification of both the possible torsion subgroups and the rational cyclic isogenies of a $K$-CM elliptic curve $E$ defined over $K\left(j\left(E\right)\right)$.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/pjm

We have not been able to recognize your IP address 3.223.3.101 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.