  We give two new examples of non-hyperelliptic curves whose Ceresa cycles have
torsion images in the intermediate Jacobian. For one of them, the central value
of the $L$-function of the relevant motive is non-vanishing and the Ceresa
cycle is torsion in the Griffiths group, consistent with the conjectures of
Beilinson and Bloch. We speculate on a possible explanation for the existence
of these torsion Ceresa classes, based on some computations with cyclic Fermat
quotients.
