Torsors under some group schemes of order pn

Let R be a complete dvr with perfect residue field k of characteristic p>0. Let {Gλ}λ∈R be the class of R-affine, commutative, smooth of relative dimension one group schemes generically isomorphic to Gm. Let be the class of finite flat commutative group schemes of order pn defined as kernels of the isogenies φλ,n:Gλ→G(λpn). We provide an explicit description of torsors over R-schemes under the group schemes Gλ and Gλ,n.