Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 2-Selmer Groups and the Birch-Swinnerton-Dyer Conjecture for the
  Congruent Number Curve   We take an approach toward counting the number of n for which the curves E_n:
y^2=x^3-n^2x have 2-Selmer groups of a given size. This question was also
discussed in a pair of Invent. Math. papers by Roger Heath-Brown. We discuss
the connection between computing the size of these Selmer groups and verifying
cases of the Birch and Swinnerton-Dyer Conjecture. The key ingredient for the
asymptotic formulae is the ``independence'' of the Legendre symbol evaluated at
the prime divisors of an integer with exactly k prime factors.

5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th