  We describe an algorithm that provably computes the rational torsion subgroup
of the Jacobian of a curve without relying on height bounds. Instead, it relies
on computing torsion points over small number fields. Both complex analytic and
Chinese remainder theorem based methods are used to find such torsion points.
The method has been implemented in Magma and used to provably compute the
rational torsion subgroup for more than 98% of Jacobians of curves in a dataset
due to Sutherland consisting of 82240 plane quartic curves.
