<< KnotTheory`

Ks=AllKnots[{0,10}];
Length[Ks]

Length[Union[Jones /@ Ks]]

c[K_] :=c[PD[K]];
c[pd_PD] := Module[{n=Length[pd], z, e,m},
z=Table[0,{2n}];
e[j_] := ReplacePart[z, j->1];
m=Join@@((List@@pd) /. X[i_,j_,k_,l_] :> {e[j]-e[l], e[i]+e[k]-e[j]});
2n-MatrixRank[m, Modulus->3]
]

Union[c /@ Rest[Ks]]