Klein's Equation

If a Real curve has no singularities except nodes and Cusps, Bitangents, and Inflection Points, then

$$n+2\tau'_2+\iota'=m+2\delta'_2+\kappa',$$

where $n$ is the order, $\tau'$ is the number of conjugate tangents, $\iota'$ is the number of Real inflections, $m$ is the class, $\delta'$ is the number of Real conjugate points, and $\kappa'$ is the number of Real Cusps. This is also called Klein's Theorem.

See also Plücker's Equation

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 114, 1959.