For integers and , we study bounds on the cardinality of the set of points of order dividing lying on a hyperelliptic curve of genus 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.
"ON THE NUMBER OF POINTS OF GIVEN ORDER ON ODD-DEGREE HYPERELLIPTIC CURVES." Rocky Mountain J. Math. 53 (2) 357 - 382, April 2023. https://doi.org/10.1216/rmj.2023.53.357