How big is the image of the Galois representations attached to CM elliptic 
curves?

Campagna, Francesco; Pengo, Riccardo

doi:10.1090/conm/779/15670

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How big is the image of the Galois representations attached to CM elliptic curves?

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Campagna, Francesco
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/conm/779/15670
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2201.04046.pdf
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Citation

Campagna, F., & Pengo, R. (2022). How big is the image of the Galois representations attached to CM elliptic curves? In Arithmetic, Geometry, Cryptography, and Coding Theory 2021 (pp. 41-56). Providence, RI: American Mathematical Society.

Cite as: https://hdl.handle.net/21.11116/0000-000A-F54B-E

Abstract

Using an analogue of Serre's open image theorem for elliptic curves with
complex multiplication, one can associate to each CM elliptic curve $E$ defined
over a number field $F$ a natural number $\mathcal{I}(E/F)$ which describes how
big the image of the Galois representation associated to $E$ is. We show how
one can compute $\mathcal{I}(E/F)$, using a closed formula that we obtain from
the classical theory of complex multiplication.