Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Good elliptic curves with a specified torsion subgroup   An elliptic curve $E$ over $\mathbb{Q}$ is said to be good if
$N_{E}^{6}<\max\!\left\{ \left\vert c_{4}^{3}\right\vert ,c_{6}^{2}\right\} $
where $N_{E}$ is the conductor of $E$ and $c_{4}$ and $c_{6}$ are the
invariants associated to a global minimal model of $E$. In this article, we
generalize Masser's Theorem on the existence of infinitely many good elliptic
curves with full $2$-torsion. Specifically, we prove via constructive methods
that for each of the fifteen torsion subgroups $T$ allowed by Mazur's Torsion
Theorem, there are infinitely many good elliptic curves $E$ with
$E\!\left(\mathbb{Q}\right) _{\text{tors}}\cong T$.

23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th