The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.
For a crunodal cubic the six inflections which disappear are two of them real, the other four imaginary, and there remain two imaginary inflections and one real inflection.
The oval may unite itself with the infinite branch, or it may dwindle into a point, and we have the crunodal and the acnodal forms respectively; or if simultaneously the oval dwindles into a point and unites itself to the infinite branch, we have the cuspidal form.
Crunodal or acnodal), or cuspidal; and we see further that there are two kinds of non-singular curves, the complex and the simplex.
There is thus a complete division into the five kinds, the complex, simplex, crunodal, acnodal and cuspidal.