Piontkowski's three-cusp conjecture for rational cuspidal plane curves

Let $C$ be a rational cuspidal plane curve of degree $d$. The source identifies three specific series of tricuspidal curves in a table. Piontkowski's conjecture. If $d\geq 6$, then $C$ has at most three cusps; moreover, the curves of degree $d\geq 6$ with precisely three cusps occur in those three series. This conjecture was proposed after investigating almost all cuspidal curves of degree at most $20$; the source does not state that it has been proved or disproved.