Some computational aspects of Jacobians of curves in the family y3=γx5+δ over Fp

  • Authors:

  • RéGis Blache;Jean-Pierre Cherdieu;Jorge Estrada Sarlabous

  • Affiliations:

  • Equipe “Géométrie algébrique et applications à la théorie de l'information,” Université de Polynésie Française, BP 6570 F98702 Faa'a, French Pol ...;Département de Mathématiques et Informatique, Université des Antilles et de la Guyane, Campus de Fouillole, F97159 Pointe-à-Pitre cedex, France;Department of Geometry, ICIMAF, Calle E No. 309, esquina 15, Vedado, La Habana, Cuba

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2007

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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.