Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Prime twists of elliptic curves   For certain elliptic curves $E/\mathbb{Q}$ with
$E(\mathbb{Q})[2]=\mathbb{Z}/2 \mathbb{Z}$, we prove a criterion for prime
twists of $E$ to have analytic rank 0 or 1, based on a mod 4 congruence of
2-adic logarithms of Heegner points. As an application, we prove new cases of
Silverman's conjecture that there exists a positive proposition of prime twists
of $E$ of rank zero (resp. positive rank).

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn