Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Neighborhood of the supersingular elliptic curve isogeny graph at $j=0$
  and $1728$   We describe the neighborhood of the vertex $[E_0]$ (resp. $[E_{1728}]$) in
the $\ell$-isogeny graph $\mathcal{G}_\ell(\mathbb{F}_{p^2}, -2p)$ of
supersingular elliptic curves over the finite field $\mathbb{F}_{p^2}$ when
$p>3\ell^2$ (resp. $p>4\ell^2$) with $E_0: y^2=x^3+1$ (resp. $E_{1728}:
y^2=x^3+x$) supersingular.

32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol