Bicuspid curve
Encyclopedia
The biscuspid is a quartic plane curve
with the equation
where a determines the size of the curve.
The bicuspid has only the two nodes as singularities, and hence is a curve of genus one.
Quartic plane curve
A quartic plane curve is a plane curve of the fourth degree. It can be defined by a quartic equation:Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0....
with the equation
where a determines the size of the curve.
The bicuspid has only the two nodes as singularities, and hence is a curve of genus one.