Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Orders of Tate-Shafarevich groups for the cubic twists of $X_0(27)$
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga