Sous-groupes de torsion d'ordres élevés de Jacobiennes décomposables de courbes de genre 2

Everett W. Howe, Franck Leprévost, and Bjorn Poonen: Sous-groupes de torsion d'ordres élevés de Jacobiennes décomposables de courbes de genre 2, C. R. Acad. Sci. Paris. Sér I Math. 323 (1996) 1031–1034, MR 97k:11097, Zbl 0895.11027.

In this announcement we summarize part of the results of a forth-coming paper (see the following listing). Our goal is to find curves of genus two, or families of curves of genus two, that are defined over Q and whose Jacobians contain large rational torsion subgroups. We give a list of the groups that we can obtain and of the type of family we get for each group. We give details for the case of the group Z/63Z, which is the largest cyclic group on our list.