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**)

**Authors:**

**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)

- 2021-07-17 11:40:23 by Andrew Sutherland
- 2021-07-17 11:38:45 by Andrew Sutherland
- 2021-07-17 11:20:27 by Andrew Sutherland
- 2021-07-17 11:16:55 by Andrew Sutherland

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