Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The quadratic character of 1+\sqrt{2} and an elliptic curve   When p is congruent to 1 mod 8, we have a criterion of the quadratic
character of 1+\sqrt{2}, which is related to the class number of \Q(\sqrt{-p}).
In this paper, we obtain a similar criterion using an elliptic curve, which
contrasts to the proof using algebraic number theory for the old one.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ