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We prove an elementary method to classify, up to rigid isotopy, all nodaldegree 4 real rational curves in $\mathbb{RP}^2$ that have only real doublepoints. We show how to associate a chord diagram to a nodal real degree 4planar rational curve and prove that such curves are defined up to rigidisotopy by their chord diagrams.

Rigid isotopy classification of real degree-4 planar rational curves with only real nodes (An elementary approach)