<< KnotTheory`

Timing[tabH=Table[K -> HOMFLYPT[Mirror@PD[K]][a,z], {K, AllKnots[{3,10}]}];]

Timing[tabJ=Table[K -> Jones[Mirror@PD[K]][q], {K, AllKnots[{3,10}]}];]

Timing[tabA=Table[K -> Alexander[Mirror@PD[K]][t], {K, AllKnots[{3,10}]}];]