Point counting on Picard curves in large characteristic
Mark L. Bauer, Edlyn Teske, Annegret Weng · Mathematics of Computation · 2005
We present an algorithm for computing the cardinality of the Jacobian of a random Picard curve over a finite field. If the underlying field is a prime field F p \mathbb {F}_p , the algorithm has complexity O ( p ) O(\sqrt {p}) .