Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modularity of some elliptic curves over totally real fields   We investigate modularity of elliptic curves over a general totally real
number field, establishing a finiteness result for the set non-modular
$j$-invariants. By analyzing quadratic points on some modular curves, we show
that all elliptic curves over certain real quadratic fields are modular.

13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int