A threaded connection design having a double ellipse in the thread root for reducing stress fatigue is illustrated in this disclosure. The root groove includes a first portion comprising a first elliptical surface being part of a first ellipse. The root groove further includes a second portion comprising a second elliptical surface, being part of a second ellipse, and the second elliptical surface being joined tangentially at a first end to the first elliptical surface at a junction point that defines the bottom of the root groove. The second elliptical surface is joined tangentially at a second end to the load flank.