Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Polynomials of Singular Moduli   Given a properly normalized parametrization of a genus-0 modular curve, the
complex multiplication points map to algebraic numbers called singular moduli.
In the classical case, the maps can be given analytically. However, in the
Shimura curve cases, no such analytical expansion is possible. Fortunately, in
both cases there are known algorithms for algebraically computing the rational
norms of the singular moduli. We demonstrate a method of using these norm
algorithms to algebraically determine the minimal polynomial of the singular
moduli below a discriminant threshold. We then use these minimal polynomials to
compute the algebraic $abc$-ratios for the singular moduli.

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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: patt-sol