For let be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve . We determine all and for which the quotient curve is rational or elliptic.
Pour désigne un sous-groupe d’involutions d’Atkin-Lehner de la courbe modulaire de Drinfeld. On détermine tous les et tels que la courbe est rationnelle ou elliptique.
@article{JTNB_1998__10_1_107_0,
author = {Andreas Schweizer},
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},
doi = {10.5802/jtnb.221},
zbl = {0930.11040},
mrnumber = {1827288},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.221/}
}
TY - JOUR
AU - Andreas Schweizer
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://jtnb.centre-mersenne.org/articles/10.5802/jtnb.221/
DO - 10.5802/jtnb.221
LA - en
ID - JTNB_1998__10_1_107_0
ER -
%0 Journal Article
%A Andreas Schweizer
%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://jtnb.centre-mersenne.org/articles/10.5802/jtnb.221/
%R 10.5802/jtnb.221
%G en
%F JTNB_1998__10_1_107_0
Andreas Schweizer. Involutory elliptic curves over $\mathbb {F}_q(T)$. Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 1, pp. 107-123. doi: 10.5802/jtnb.221
[A&L] and , Hecke Operators on Γ0(m), Math. Annalen 185 (1970), 134-160. | Zbl
[Ge1] , Drinfeld-Moduln und modulare Formen über rationalen Funktionenkörpem, Bonner Mathematische Schriften 119 (1980). | MR | Zbl
[Ge2] , Automorphe Formen über Fq (T) mit kleinem Führer, Abh. Math. Sem. Univ. Hamburg 55 (1985), 111-146. | MR | Zbl
[Ge3] , Analytical Construction of Weil Curves over Function Fields, J. Théor. Nombres Bordeaux 7 (1995), 27-49. | Numdam | MR | Zbl
[G&N] and , Fundamental domains of some arithmetic groups over function fields, Internat. J. Math. 6 (1995), 689-708. | MR | Zbl
[G&R] and , Jacobians of Drinfeld Modular Curves, J. Reine Angew. Math. 476 (1996), 27-93. | MR | Zbl
[Ke] , A note on involutory Weil curves, Quat. J. Math. Oxford (Ser. 2) 27 (1976), 401-405. | MR | Zbl
[Kl] , On the normalizer of ro(N). Modular Functions of one Variable V, Springer LNM 601, Berlin Heidelberg New York 1977, 239-246. | MR | Zbl
[M&SD] and , Arithmetic of Weil Curves, Invent. Math. 25 (1974), 1-61. | MR | Zbl
[Sch1] , Zur Arithmetik der Drinfeld'schen Modulkurven X0(n), Dissertation, Saarbrücken 1996
[Sch2] , Modular automorphisms of the Drinfeld modular curves X0(n), Collect. Math. 48 (1997), 209-216. | MR | Zbl
[Sch3] , 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 | MR | Zbl
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