Classification of real rational knots of low degree in the 3-sphere

In this paper, we classify, up to rigid isotopy, real rational knots of degrees less than or equal to [Formula: see text] in a real quadric homeomorphic to the 3-sphere. We also study their connections with rigid isotopy classes of real rational knots of low degree in [Formula: see text] and classify real rational curves of degree 6 in the 3-sphere with exactly one ordinary double point.