Title: Frobenius elements in Galois representations with SL_n image,
Abstract: Suppose we have a elliptic curve over a number field whose mod $l$
representation has image isomorphic to $SL_2(\mathbb{F}_l)$. We present a
method to determine Frobenius elements of the associated Galois group which
incorporates the linear structure available. We are able to distinguish
$SL_n(\mathbb{F}_l)$-conjugacy from $GL_n(\mathbb{F}_l)$-conjugacy; this can be
thought of as being analogous to a result which distinguishes $A_n$-conjugacy
from $S_n$-conjugacy when the Galois group is considered as a permutation
group.