Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heegner Points on Modular Curves   In this paper, we study the Heegner points on more general modular curves
other than $X_0(N)$, which generalizes Gross' work "Heegner points on
$X_0(N)$". The explicit Gross-Zagier formula and the Euler system property are
stated in this case. Using such kind of Heegner points, we construct certain
families of quadratic twists of $X_0(36)$, with the ranks of Mordell-Weil
groups being zero and one respectively, and show that the $2$-part of their BSD
conjectures hold.

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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an