AN AFFINE MODEL OF X0(mn)

Title & Authors
AN AFFINE MODEL OF X0(mn)
Choi, So-Young; Koo, Ja-Kyung;

Abstract
We show that the modular equation $\small{{\phi}^{T_n}_m}$ (X, Y) for the Thompson series $\small{T_n}$ corresponding to $\small{{\Gamma}_0}$(n) gives an affine model of the modular curve $\small{X_0}$(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of $\small{T_n(z)\;and\;T_n}$(mz).
Keywords
modular curve;modular equation;class field;
Language
English
Cited by
1.
AN AFFINE MODEL OF X0(pq)+q,;

충청수학회지, 2013. vol.26. 3, pp.641-645
1.
AN AFFINE MODEL OF X0(pq)+q, Journal of the Chungcheong Mathematical Society, 2013, 26, 3, 641
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