English

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}
}