<< KnotTheory`

L=PD[
X[12,6,1,5], X[8,2,9,1], X[4,10,5,9],
X[18,3,13,2],X[3,14,4,13], X[14,11,15,10],
X[11,16,12,15], X[16,7,17,6], X[7,18,8,17]
];

j=Jones[L][q]

maybe=Select[AllLinks[], (
quo=Factor[(Jones[#][q]/j)];
quo==1 || quo==q || MatchQ[quo, q^_]
)&]

mva=MultivariableAlexander[L][t]

MultivariableAlexander[#][t]& /@ maybe

DrawMorseLink[Link["L9n15"]]