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Working over an algebraically closed field of arbitrary characteristic westudy, for integers $N\geq 2$ and $g\geq 2$, the set of points of orderdividing $N$ lying on an irreducible smooth proper curve of genus $g$ embeddedin its jacobian using a fixed base point. We discuss bounds on its cardinalityand describe an efficient method for computing the set. Our method useswronskians similar to those used in the study of Weierstrass points and thestrength of our bounds is related to whether or not a certain multiple of thecurve is contained in the negative of the theta divisor. Several examples arediscussed. This generalizes our previous work[https://doi.org/10.1216/rmj.2023.53.357] dealing with the case ofhyperelliptic curves embedded in their jacobian using a Weierstrass point asbase point.

Bounds on the number of torsion points of given order on curves embedded in their jacobians