Binary quartic
= Binary quartic
{title2=$f(X,Y)=\sum_{j=0}^4 a_jX^{4-j}Y^j$}
A <binary quartic> is a homogeneous degree-four <polynomial> in two variables. Over the complex numbers it determines four points of the <projective line>, counted with multiplicity. Its <discriminant> is nonzero exactly when the four points are distinct; this is also its <geometric invariant theory> stability condition under $SL_2$.