Non-elliptic Shimura curves of genus one

GONZÁLEZ, Josep; ROTGER, Victor

J. Math. Soc. Japan, Tome 58 (2006) no. 3, p. 927-948 / Harvested from Project Euclid

Résumé

We present explicit models for non-elliptic genus one Shimura curves $X_0(D, N)$ with $\Gamma_0(N)$ -level structure arising from an indefinite quaternion algebra of reduced discriminant $D$ , and Atkin-Lehner quotients of them. In addition, we discuss and extend Jordan's work [10, Ch. III] on points with complex multiplication on Shimura curves.

Publié le : 2006-10-14
Classification: Shimura curve, curve of genus one, elliptic curve, complex multiplication points, 11G18, 14G35

@article{1179759530,
     author = {GONZ\'ALEZ, Josep and ROTGER, Victor},
     title = {Non-elliptic Shimura curves of genus one},
     journal = {J. Math. Soc. Japan},
     volume = {58},
     number = {3},
     year = {2006},
     pages = { 927-948},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1179759530}
}

GONZÁLEZ, Josep; ROTGER, Victor. Non-elliptic Shimura curves of genus one. J. Math. Soc. Japan, Tome 58 (2006) no. 3, pp.  927-948. http://gdmltest.u-ga.fr/item/1179759530/