show · ec.galois_rep_elladic_image all knowls · up · search:

Let $\ell$ be a prime and let $E$ be an elliptic curve over $\Q$ that does not have potential complex multiplication.

Subgroups $G$ of $\GL(2,\Z_\ell)$ that can arise as the $\ell$-adic image $H$ of the $\ell$-adic Galois representation \[ \rho_{E,\ell}\colon {\Gal}(\overline{\Q}/\Q)\to \GL(2,\Z_\ell) \] attached to $E$ are identified using the labels introduced by Rouse, Sutherland, and Zureick-Brown in [arXiv:/2106.11141 ]. These labels have the form \[ \mathbf{N.i.g.n}, \] where N is is the level of $H$, i is the index of $H$, g is the genus of $H$, and n is an ordinal that distinguishes groups of the same level, index, and genus (see Section 2 of [arXiv:2106.11141 ] for details on the ordering that is used to define n)

Knowl status:
  • Review status: beta
  • Last edited by Andrew Sutherland on 2021-07-17 11:40:23
Referred to by:

Not referenced anywhere at the moment.

History: (expand/hide all) Differences (show/hide)