Explicit ℓ-Sylow of genus 2 curves over finite fields

In this paper we extend an algorithm by Miret, Pujolàs and Rio to compute generators of the [Formula: see text]-Sylow subgroup of the Jacobian of genus [Formula: see text] curves over finite fields, to cover primes [Formula: see text] and hyperelliptic curves of genus [Formula: see text]. Our algorithm is quicker as it starts from [Formula: see text] divisors instead of the whole [Formula: see text]. The outcomes for several trial curves for [Formula: see text] and [Formula: see text] indicate it may lead to speedups in point counting for genus [Formula: see text] curves.