TY - JOUR
T1 - On Drinfeld modular curves for SL(2)
AU - Franklin, Jesse
AU - Ho, Sheng Yang Kevin
AU - Papikian, Mihran
N1 - Publisher Copyright:
© 2025 World Scientific Publishing Company.
PY - 2025/10/1
Y1 - 2025/10/1
N2 - In this paper, we study the Drinfeld modular curves X01(n) arising from the Hecke congruence subgroups of SL2(Fq[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 X01(n) 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 X01(n).
AB - In this paper, we study the Drinfeld modular curves X01(n) arising from the Hecke congruence subgroups of SL2(Fq[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 X01(n) 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 X01(n).
UR - https://www.scopus.com/pages/publications/105014011792
UR - https://www.scopus.com/inward/citedby.url?scp=105014011792&partnerID=8YFLogxK
U2 - 10.1142/S0129167X25500442
DO - 10.1142/S0129167X25500442
M3 - Article
AN - SCOPUS:105014011792
SN - 0129-167X
VL - 36
JO - International Journal of Mathematics
JF - International Journal of Mathematics
IS - 12
M1 - 2550044
ER -