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On Drinfeld modular curves for SL(2).

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Bibliographic Details
Title: On Drinfeld modular curves for SL(2).
Authors: Franklin, Jesse1 (AUTHOR) jfranklin1185@gmail.com, Ho, Sheng-Yang Kevin2 (AUTHOR) kevinho@ucsd.edu, Papikian, Mihran3 (AUTHOR) papikian@psu.edu
Source: International Journal of Mathematics. Oct2025, Vol. 36 Issue 12, p1-35. 35p.
Subject Terms: *ELLIPTIC curves, *MODULAR forms, *MODULAR groups, *COMBINATORICS, *MATHEMATICAL formulas
Abstract: In this paper, we study the Drinfeld modular curves X 0 1 () arising from the Hecke congruence subgroups of S L 2 ( q [ T ]). By using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. Then, in cases when the genus of X 0 1 () is one, we compute the Weierstrass equation of the corresponding curve. Finally, we define and study the modular polynomial in this context, which gives a plane singular model of X 0 1 (). [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:In this paper, we study the Drinfeld modular curves X 0 1 () arising from the Hecke congruence subgroups of S L 2 ( q [ T ]). By using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. Then, in cases when the genus of X 0 1 () is one, we compute the Weierstrass equation of the corresponding curve. Finally, we define and study the modular polynomial in this context, which gives a plane singular model of X 0 1 (). [ABSTRACT FROM AUTHOR]
ISSN:0129167X
DOI:10.1142/S0129167X25500442