<< KnotTheory`

MonomialQ[c_] /; FreeQ[c,t] := True;
MonomialQ[c_. t] /; FreeQ[c,t] := True;
MonomialQ[c_. (t^(_))] /; FreeQ[c,t] := True;
MonomialQ[_]=False;
FMQ[m_] /; MonomialQ[m] := True;
FMQ[r_] /; !MonomialQ[Denominator[r]] := False;
FMQ[p_] := Module[{fp=Factor[p],fac},
fp=Select[fp,(!MonomialQ[#])&];
If[!MatchQ[Head[fp],Times|Power], False,
fac=FactorList[fp][[2,1]];
FMQ[Together[(fp/(fac(fac/.t->1/t)))]]]
]

l11=Select[AllKnots[{3,11}], FMQ[Alexander[#][t]]&]

Alexander[Knot[10,98]][t] // Factor

KnotSignature[Knot[10,98]]

KnotSignature /@ l11