The a-numbers of Jacobians of Suzuki curves

For \(m \in {\mathbb N}\), let \(S_m\) be the Suzuki curve defined over \({\mathbb F}_{2^{2m+1}}\). It is well-known that \(S_m\) is supersingular, but the p-torsion group scheme of its Jacobian is not known. The a-number is an invariant of the isomorphism class of the p-torsion group scheme. In this paper, we compute a closed formula for the a-number of \(S_m\) using the action of the Cartier operator on \(H^0(S_m,\Omega^1)\).