## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Elliptic $\mod \ell$ Galois representations which are not minimally elliptic

Luis Dieulefait

#### Abstract

In a recent preprint (see [C]), F. Calegari has shown that for $\ell = 2, 3, 5$ and $7$ there exist $2$-dimensional irreducible representations $\rho$ of Gal$(\bar{\Q}/\Q)$ with values in $\F_\ell$ coming from the $\ell$-torsion points of an elliptic curve defined over $\Q$, but not minimally, i.e., so that any elliptic curve giving rise to $\rho$ has prime-to-$\ell$ conductor greater than the (prime-to-$\ell$) conductor of $\rho$. In this brief note, we will show that the same is true for any prime $\ell >7$

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 3 (2006), 455-457.

Dates
First available in Project Euclid: 20 October 2006

https://projecteuclid.org/euclid.bbms/1161350686

Digital Object Identifier
doi:10.36045/bbms/1161350686

Mathematical Reviews number (MathSciNet)
MR2307680

Zentralblatt MATH identifier
1124.11025

#### Citation

Dieulefait, Luis. Elliptic $\mod \ell$ Galois representations which are not minimally elliptic. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 3, 455--457. doi:10.36045/bbms/1161350686. https://projecteuclid.org/euclid.bbms/1161350686