Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting rational points on elliptic curves with a rational 2-torsion
  point   Let $E/\mathbb{Q}$ be an elliptic curve over the rational numbers. It is
known, by the work of Bombieri and Zannier, that if $E$ has full rational
$2$-torsion, the number $N_E(B)$ of rational points with Weil height bounded by
$B$ is $\exp\left(O\left(\frac{\log B}{\sqrt{\log\log B}}\right)\right)$. In
this paper we exploit the method of descent via $2$-isogeny to extend this
result to elliptic curves with just one nontrivial rational $2$-torsion point.
Moreover, we make use of a result of Petsche to derive the stronger upper bound
$N_{E}(B) = \exp\left(O\left(\frac{\log B}{\log\log B}\right)\right)$ for these
curves and to remove a deep transcendence theory ingredient from the proof.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th