Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic curves with large torsion and positive rank over number fields
  of small degree and ECM factorization   In this paper, we present several methods for construction of elliptic curves
with large torsion group and positive rank over number fields of small degree.
We also discuss potential applications of such curves in the elliptic curve
factorization method (ECM).

22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga