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arXiv · 2408.04159

Models of CM elliptic curves with a prescribed $\ell$-adic Galois image

Enrique González-Jiménez·Álvaro Lozano-Robledo·Benjamin York
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Abstract

For each prime number $\ell$ and for each imaginary quadratic order of class number one or two, we determine all the possible $\ell$-adic Galois representations that occur for any elliptic curve with complex multiplication by such an order over its minimal field of definition, and then we determine all the isomorphism classes of elliptic curves that have a prescribed $\ell$-adic Galois representation.

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Enrique González-Jiménez, Álvaro Lozano-Robledo, Benjamin York. 2025-05-22. Models of CM elliptic curves with a prescribed $\ell$-adic Galois image. https://doi.org/10.1016/j.jnt.2025.03.001

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