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Models of CM elliptic curves with a prescribed ℓ-adic Galois image

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Název: Models of CM elliptic curves with a prescribed ℓ-adic Galois image
Autoři: Enrique González–Jiménez, Álvaro Lozano-Robledo, Benjamin York
Zdroj: Journal of Number Theory. 277:19-62
Publication Status: Preprint
Informace o vydavateli: Elsevier BV, 2025.
Rok vydání: 2025
Témata: Mathematics - Number Theory, FOS: Mathematics, Primary: 11G05, Secondary: 11G15, 14H52, 14K22, Number Theory (math.NT)
Popis: 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.
38 pages; this new version adds bibliographic information for published version and fixes some minor typos
Druh dokumentu: Article
Jazyk: English
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2025.03.001
DOI: 10.48550/arxiv.2408.04159
Přístupová URL adresa: http://arxiv.org/abs/2408.04159
Rights: Elsevier TDM
CC BY
Přístupové číslo: edsair.doi.dedup.....a33cc9ae4637b0468ca065623f959e85
Databáze: OpenAIRE
Popis
Abstrakt: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.<br />38 pages; this new version adds bibliographic information for published version and fixes some minor typos
ISSN:0022314X
DOI:10.1016/j.jnt.2025.03.001