Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level raising mod 2 and arbitrary 2-Selmer ranks   We prove a level raising mod $\ell=2$ theorem for elliptic curves over
$\mathbb{Q}$. It generalizes theorems of Ribet and Diamond-Taylor and also
explains different sign phenomena compared to odd $\ell$. We use it to study
the 2-Selmer groups of modular abelian varieties with common mod 2 Galois
representation. As an application, we show that the 2-Selmer rank can be
arbitrary in level raising families.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph