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arXiv · 2110.07819

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

Abbey Bourdon·Holly Paige Chaos
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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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Abbey Bourdon, Holly Paige Chaos. 2021-10-15. Torsion for CM elliptic curves defined over number fields of degree 2p. https://arxiv.org/abs/2110.07819

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