The relation between two terminology "cusp" (group & algebraic curve) Dear Folks: I come across the word "cusp" in two different fields and I think they are related. Could anyone specify their relationship for me?? Many thanks!! the cusp of an algebraic curve: for example: (0,0) is the cusp of the complex algebraic curve y2=x3; the cusp point of a discrete group of SL(2,R) , where SL(2,R) acts on the upper half plane by linear fractional transformation. This terminology usually appears when we talk about modular forms.