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Conference Paper

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

##### External Resource

https://doi.org/10.1090/conm/779/15670

(Publisher version)

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##### Fulltext (public)

2201.04046.pdf

(Preprint), 512KB

##### Supplementary Material (public)

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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.

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.