Pensieve header: Analyzing a knot suggested by David Vincent.

<< KnotTheory`

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

?Jones

J=Jones[K][q]

{K1}=Select[AllKnots[{3,8}], Jones[#][q]==J&]

From http://katlas.org/wiki/8_ 14:

Jones[K1][q]

?Alexander

{Alexander[K][t], Alexander[K1][t]}

?HOMFLYPT

{HOMFLYPT[K][a,q], HOMFLYPT[K1][a,q]}

?Kh

{Kh[K][q,t], Kh[K1][q,t]} // Column