K13n3921

Knot presentations

Dowker-Thistlethwaite code

6 8 18 20 4 -16 -26 -22 -24 2 -14 -10 -12

Notes on presentations of K13n3921

Polynomial invariants

Jones polynomial	Data:K13n3921/Jones Polynomial
Alexander polynomial	$-t^{3}+5t^{2}-11t+15-11t^{-1}+5t^{-2}-t^{-3}$
Conway polynomial	Data:K13n3921/Conway Polynomial
Determinant	49
Signature	0
HOMFLY-PT polynomial	$z^{8}a^{-2}-z^{8}+a^{2}z^{6}+6z^{6}a^{-2}-z^{6}a^{-4}-7z^{6}+4a^{2}z^{4}+13z^{4}a^{-2}-3z^{4}a^{-4}-15z^{4}+4a^{2}z^{2}+11z^{2}a^{-2}-3z^{2}a^{-4}-12z^{2}+a^{2}+3a^{-2}-a^{-4}-2$
Kauffman polynomial	$az^{11}+2z^{11}a^{-1}+z^{11}a^{-3}+3a^{2}z^{10}+6z^{10}a^{-2}+4z^{10}a^{-4}+5z^{10}+3a^{3}z^{9}-3az^{9}-9z^{9}a^{-1}+3z^{9}a^{-3}+6z^{9}a^{-5}+a^{4}z^{8}-18a^{2}z^{8}-35z^{8}a^{-2}-12z^{8}a^{-4}+4z^{8}a^{-6}-38z^{8}-17a^{3}z^{7}-17az^{7}-7z^{7}a^{-1}-30z^{7}a^{-3}-22z^{7}a^{-5}+z^{7}a^{-7}-5a^{4}z^{6}+26a^{2}z^{6}+60z^{6}a^{-2}+z^{6}a^{-4}-14z^{6}a^{-6}+76z^{6}+25a^{3}z^{5}+47az^{5}+45z^{5}a^{-1}+44z^{5}a^{-3}+18z^{5}a^{-5}-3z^{5}a^{-7}+6a^{4}z^{4}-13a^{2}z^{4}-45z^{4}a^{-2}+2z^{4}a^{-4}+11z^{4}a^{-6}-55z^{4}-13a^{3}z^{3}-31az^{3}-36z^{3}a^{-1}-27z^{3}a^{-3}-7z^{3}a^{-5}+2z^{3}a^{-7}-2a^{4}z^{2}+4a^{2}z^{2}+17z^{2}a^{-2}+2z^{2}a^{-4}-2z^{2}a^{-6}+19z^{2}+2a^{3}z+6az+8za^{-1}+6za^{-3}+2za^{-5}-a^{2}-3a^{-2}-a^{-4}-2$

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