Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A formula for the Selmer group of a rational three-isogeny   A formula is given for the dimension of the Selmer group of the rational
three-isogeny of elliptic curves of the form y^2=x^3+a(x-b)^2. The formula is
in terms of the three-ranks of the quadratic number fields Q(\sqrt{a}) and
Q(\sqrt{-3a}) and various aspects of the arithmetic of these number fields. In
addition a duality theorem is used to relate the dimension of the Selmer group
of the three-isogeny with the dimension of the Selmer group of its dual
isogeny.

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The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an