On the number of point of given order on odd degree hyperelliptic curves

Abstract

For integers $N\ge 3$ and $g\ge 1$, we study bounds on the cardinality of the set of points of order dividing $N$ lying on a hyperelliptic curve of genus $g$ embedded in its jacobian using a Weierstrass point as base point. This leads us to revisit division polynomials introduced by Cantor in 1995 and strengthen a divisibility result proved by him. Several examples are discussed.

Close to accepted version

References in corpus (1)

• Torsion Points of order 2g+1 on odd degree hyperelliptic curves of genus g