<< KnotTheory`

(# -> KnotDet[#])& /@ AllKnots[{3,7}]

k9=Select[AllKnots[{3,10}], Divisible[KnotDet[#], 9]&]

(# -> KnotDet[#])& /@ k9

Tri[K_] := 3((Abs[Jones[K][(E^(2π I/6))]])^2)

Tri[Knot[3,1]]

(# -> Tri[#])& /@ k9

Tri[Knot[4,1]]