  For integers $N\geq 3$ and $g\geq 1$, 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.
