The coordinate and spectral integral representations of Hamiltonian in isotropic LandauLifschitz equation are given by a standard procedure.But,the problem of deriving the corresponding conserved quantity to connect two kinds of integral mentioned above is still open.In this paper,using the gauge invariance properties,the compatibility pair of LL equation is transformed to the form-ikσ3+O(1) by choosing an app ropriate tr ansformation.Hence,the conserved quantities are obtained.The zeroth conserved qu antity,I0,is zero.The first one,I1,which has coordinate an d spe ctral integral representations,coincide with the two desired integral representations of the Hamiltonian.