2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159710We give two numerical methods for computing the first bifurcation point for Delaunay nodoids. With regard to methods for constructing constant mean curvature surfaces, we conclude that the bifurcation point in the analytic method of Mazzeo-Pacard is the same as a limiting point encountered in the integrable systems method of Dorfmeister-Pedit-Wu.v2: one statement in the introduction corrected, section on Jacobi functions addedDifferential Geometry53A10text