## Entanglement in the family of division fields of elliptic curves with complex multiplication

Publikation: Working paperForskning

### Dokumenter

For every CM elliptic curve $E$ defined over a number field $F$ containing the CM field $K$, we prove that the family of $p^{\infty}$-division fields of $E$, with $p \in \mathbb{N}$ prime, becomes linearly disjoint over $F$ after removing an explicit finite subfamily of fields. If $F = K$ and $E$ is obtained as the base-change of an elliptic curve defined over $\mathbb{Q}$, we prove that this finite subfamily is never linearly disjoint over $K$ as soon as it contains more than one element.
Originalsprog Engelsk arXiv preprint Ikke-udgivet - 1 jun. 2020
Navn arXiv

### Forskningsområder

• math.NT, Primary: 11G05, 14K22, 11G15, Secondary: 11S15, 11F80