Some Computational Aspects of Jacobians of Curves in the Family $y^3 = \gamma x^5 + \delta$ Over $|F_p$

Régis Blache , Jean-Pierre Cherdieu , Jorge Estrada Sarlabous

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 19

MSC 2000

14H45 Special curves and curves of low genus

14H40 Jacobians, Prym varieties

ZDM: 14H05

PACS: 14Q20, 11G10, 11T71

CR: 14Q05

Abstract
In this paper, we study the Jacobian varieties of certain diagonal curves of genus four : we first give the structure of the Jacobian, showing that it is simple over the prime field in most cases, then we give a reduction algorithm, suitable for calculations in the group of its rational points.