Torsion for CM elliptic curves defined over number fields of degree 2p
Number Theory
2022-06-09 v2 Algebraic Geometry
Abstract
For a prime number p, we characterize the groups that may arise as torsion subgroups of an elliptic curve with complex multiplication defined over a number field of degree 2p. In particular, our work shows that a classification in the strongest sense is tied to determining whether there exist infinitely many Sophie Germain primes.
Keywords
Cite
@article{arxiv.2110.07819,
title = {Torsion for CM elliptic curves defined over number fields of degree 2p},
author = {Abbey Bourdon and Holly Paige Chaos},
journal= {arXiv preprint arXiv:2110.07819},
year = {2022}
}