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arXiv · 2201.04046

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

Francesco Campagna·Riccardo Pengo
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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.

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Francesco Campagna, Riccardo Pengo. 2022-01-11. How big is the image of the Galois representations attached to CM elliptic curves?. https://doi.org/10.1090/conm%2F779%2F15670

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