Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Mordell-Weil bases for the elliptic curve of the form
  $\boldsymbol{y^2=x^3-m^2x+n^2}$   Let $E_{m,n}$ be an elliptic curve over $\mathbb{Q}$ of the form
$y^2=x^3-m^2x+n^2$, where $m$ and $n$ are positive integers. Brown and Myers
showed that the curve $E_{1,n}$ has rank at least two for all $n$. In the
present paper, we specify the two points which can be extended to a basis for
$E_{1,n}(\mathbb{Q})$ under certain conditions described explicitly. Moreover,
we verify a similar result for the curve $E_{m,1}$, which, however, gives a
basis for the rank three part of $E_{m,1}(\mathbb{Q})$.

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The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
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The categories of this paper are: supr-con