If there is a 
 correspondence between two curves of curve genus 
 and 
 and the number of branch points
 properly counted are 
 and 
,
 then
Zeuthen's Theorem
See also
Chasles-Cayley-Brill FormulaExplore with Wolfram|Alpha
References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 246, 1959.Referenced on Wolfram|Alpha
Zeuthen's TheoremCite this as:
Weisstein, Eric W. "Zeuthen's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ZeuthensTheorem.html
 
         
	    
	
    
