Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum dynamics of elliptic curves   We calculate the $K$-theory of a crossed product $C^*$-algebra
$\mathscr{A}_{RM}\rtimes\mathscr{E}(K)$, where $\mathscr{A}_{RM}$ is the
noncommutative torus with real multiplication and $\mathscr{E}(K)$ is an
elliptic curve over the number field $K$. We use this result to evaluate the
rank and the Shafarevich-Tate group of $\mathscr{E}(K)$.

36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol