Models of CM elliptic curves with a prescribed $\ell$-adic Galois image
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909620146012160 |
|---|---|
| author | González-Jiménez, Enrique Lozano-Robledo, Álvaro York, Benjamin |
| author_facet | González-Jiménez, Enrique Lozano-Robledo, Álvaro York, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04159 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Models of CM elliptic curves with a prescribed $\ell$-adic Galois image González-Jiménez, Enrique Lozano-Robledo, Álvaro York, Benjamin Number Theory Primary: 11G05, Secondary: 11G15, 14H52, 14K22 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. |
| title | Models of CM elliptic curves with a prescribed $\ell$-adic Galois image |
| topic | Number Theory Primary: 11G05, Secondary: 11G15, 14H52, 14K22 |
| url | https://arxiv.org/abs/2408.04159 |