Torsion for CM elliptic curves defined over number fields of degree 2𝑝

Bourdon, Abbey; Chaos, Holly Paige

doi:10.1090/proc/16170

Torsion for CM elliptic curves defined over number fields of degree $2p$
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by Abbey Bourdon and Holly Paige Chaos;

Proc. Amer. Math. Soc. 151 (2023), 1001-1015

DOI: https://doi.org/10.1090/proc/16170

Published electronically: December 15, 2022

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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.

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