Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cartan images and $\ell$-torsion points of elliptic curves with rational
  $j$-invariant   Let $\ell$ be an odd prime and $d$ a positive integer. We determine when
there exists a degree-$d$ number field $K$ and an elliptic curve $E/K$ with
$j(E)\in\mathbb{Q}\setminus\{0,1728\}$ for which $E(K)_{\mathrm{tors}}$
contains a point of order $\ell$. We also determine when there exists such a
pair $(K,E)$ for which the image of the associated mod-$\ell$ Galois
representation is contained in a Cartan subgroup or its normalizer,
conditionally on a conjecture of Sutherland. We do the same under the stronger
assumption that $E$ is defined over $\mathbb{Q}$.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex