Abbey Bourdon, Holly Paige Chaos
Published 2021-10-15, updated 2022-06-07Version 2
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.
CM elliptic curves and vertically entangled 2-adic groups
The density and distribution of CM elliptic curves over $\mathbb{Q}$
Bad reduction of genus $3$ curves with complex multiplication
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