Meicatalecticizant would more completely express the meaning of that which, for the sake of brevity, I denominate the catalecticant.
For binary quartics the catalecticant vanishes when the form is a sum of two 4th powers.
For a ternary quartic the catalecticant vanishes when the form is a sum of five 4th powers.
For quaternary quartics the catalecticant vanishes when the form is a sum of nine 4th powers.
For quinary quartics the catalecticant vanishes when the form is a sum of fourteen 4th powers.