Chasles-Cayley-Brill Formula

The number of coincidences of a $(\nu,\nu')$ correspondence of value $\gamma$ on a curve of Genus $p$ is given by

$$\nu+\nu'+2p\gamma.$$

See also Zeuthen's Theorem

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 129, 1959.