no. 1
Involutory elliptic curves over 𝔽 q (T)
Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 1, pp. 107-123

For n∈𝔽 q [T] let G be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve X 0 (𝔫). We determine all 𝔫 and G for which the quotient curve G∖X 0 (𝔫) is rational or elliptic.

Pour 𝔫∈𝔽 q [T],G désigne un sous-groupe d’involutions d’Atkin-Lehner de la courbe modulaire X 0 (𝔫) de Drinfeld. On détermine tous les 𝔫 et G tels que la courbe G∖X 0 (𝔫) est rationnelle ou elliptique.

@article{JTNB_1998__10_1_107_0,
     author = {Schweizer, Andreas},
     title = {Involutory elliptic curves over $\mathbb {F}_q(T)$},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {107--123},
     year = {1998},
     publisher = {Universit\'e Bordeaux I},
     volume = {10},
     number = {1},
     mrnumber = {1827288},
     zbl = {0930.11040},
     language = {en},
     url = {https://www.numdam.org/item/JTNB_1998__10_1_107_0/}
}
TY  - JOUR
AU  - Schweizer, Andreas
TI  - Involutory elliptic curves over $\mathbb {F}_q(T)$
JO  - Journal de théorie des nombres de Bordeaux
PY  - 1998
SP  - 107
EP  - 123
VL  - 10
IS  - 1
PB  - Université Bordeaux I
UR  - https://www.numdam.org/item/JTNB_1998__10_1_107_0/
LA  - en
ID  - JTNB_1998__10_1_107_0
ER  - 
%0 Journal Article
%A Schweizer, Andreas
%T Involutory elliptic curves over $\mathbb {F}_q(T)$
%J Journal de théorie des nombres de Bordeaux
%D 1998
%P 107-123
%V 10
%N 1
%I Université Bordeaux I
%U https://www.numdam.org/item/JTNB_1998__10_1_107_0/
%G en
%F JTNB_1998__10_1_107_0
Schweizer, Andreas. Involutory elliptic curves over $\mathbb {F}_q(T)$. Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 1, pp. 107-123. https://www.numdam.org/item/JTNB_1998__10_1_107_0/

[A&L] A.O. Atkin and J. Lehner, Hecke Operators on Γ0(m), Math. Annalen 185 (1970), 134-160. | Zbl

[Ge1] E.-U. Gekeler, Drinfeld-Moduln und modulare Formen über rationalen Funktionenkörpem, Bonner Mathematische Schriften 119 (1980). | Zbl | MR

[Ge2] E.-U. Gekeler, Automorphe Formen über Fq (T) mit kleinem Führer, Abh. Math. Sem. Univ. Hamburg 55 (1985), 111-146. | Zbl | MR

[Ge3] E.-U. Gekeler, Analytical Construction of Weil Curves over Function Fields, J. Théor. Nombres Bordeaux 7 (1995), 27-49. | Zbl | MR | Numdam

[G&N] E.-U. Gekeler and U. Nonnengardt, Fundamental domains of some arithmetic groups over function fields, Internat. J. Math. 6 (1995), 689-708. | Zbl | MR

[G&R] E.-U. Gekeler and M. Reversat, Jacobians of Drinfeld Modular Curves, J. Reine Angew. Math. 476 (1996), 27-93. | Zbl | MR

[Ke] M. Kenku, A note on involutory Weil curves, Quat. J. Math. Oxford (Ser. 2) 27 (1976), 401-405. | Zbl | MR

[Kl] P.G. Kluit, On the normalizer of ro(N). Modular Functions of one Variable V, Springer LNM 601, Berlin Heidelberg New York 1977, 239-246. | Zbl | MR

[M&SD] B. Mazur and P. Swinnerton-Dyer, Arithmetic of Weil Curves, Invent. Math. 25 (1974), 1-61. | Zbl | MR

[Sch1] A. Schweizer, Zur Arithmetik der Drinfeld'schen Modulkurven X0(n), Dissertation, Saarbrücken 1996

[Sch2] A. Schweizer, Modular automorphisms of the Drinfeld modular curves X0(n), Collect. Math. 48 (1997), 209-216. | Zbl | MR

[Sch3] A. Schweizer, Hyperelliptic Drinfeld Modular Curves, in: Drinfeld modules, modular schemes and applications, Proceedings of a workshop at Alden Biesen, September 9-14, 1996, (E.-U. Gekeler, M. van der Put, M. Reversat, J. Van Geel, eds.), World Scientific, Singapore, 1997, pp. 330-343 | Zbl | MR