Embedding Degree of Hyperelliptic Curves with Complex Multiplication

2007/05/10 by Ravnshoj, Christian Robenhagen
#14H40 (Primary) 14Q05 #94A60 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0705.1443

Abstract

Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect to l is one.

Related

• Isogenous hyperelliptic and non-hyperelliptic Jacobians with maximal complex multiplication
• Non-Cyclic Subgroups of Jacobians of Genus Two Curves with Complex Multiplication
• p-torsion of Genus Two Curves Over Prime Fields of Characteristic p
• Large Cyclic Subgroups of Jacobians of Hyperelliptic Curves
• Division by 2 on hyperelliptic curves and jacobians