K13a1731

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a1731

Polynomial invariants

Jones polynomial	Data:K13a1731/Jones Polynomial
Alexander polynomial	$-t^{5}+7t^{4}-23t^{3}+49t^{2}-74t+85-74t^{-1}+49t^{-2}-23t^{-3}+7t^{-4}-t^{-5}$
Conway polynomial	Data:K13a1731/Conway Polynomial
Determinant	393
Signature	0
HOMFLY-PT polynomial	$-z^{10}+a^{2}z^{8}+2z^{8}a^{-2}-6z^{8}+4a^{2}z^{6}+8z^{6}a^{-2}-z^{6}a^{-4}-13z^{6}+4a^{2}z^{4}+8z^{4}a^{-2}-2z^{4}a^{-4}-9z^{4}-a^{2}z^{2}-z^{2}a^{-2}+4z^{2}-2a^{2}-2a^{-2}+5$
Kauffman polynomial	$3z^{12}a^{-2}+3z^{12}+10az^{11}+22z^{11}a^{-1}+12z^{11}a^{-3}+15a^{2}z^{10}+35z^{10}a^{-2}+19z^{10}a^{-4}+31z^{10}+15a^{3}z^{9}+7az^{9}-24z^{9}a^{-1}-z^{9}a^{-3}+15z^{9}a^{-5}+11a^{4}z^{8}-14a^{2}z^{8}-107z^{8}a^{-2}-43z^{8}a^{-4}+6z^{8}a^{-6}-83z^{8}+5a^{5}z^{7}-21a^{3}z^{7}-43az^{7}-38z^{7}a^{-1}-58z^{7}a^{-3}-36z^{7}a^{-5}+z^{7}a^{-7}+a^{6}z^{6}-19a^{4}z^{6}-9a^{2}z^{6}+92z^{6}a^{-2}+22z^{6}a^{-4}-11z^{6}a^{-6}+70z^{6}-8a^{5}z^{5}+4a^{3}z^{5}+37az^{5}+61z^{5}a^{-1}+58z^{5}a^{-3}+21z^{5}a^{-5}-z^{5}a^{-7}-a^{6}z^{4}+10a^{4}z^{4}+14a^{2}z^{4}-20z^{4}a^{-2}-z^{4}a^{-4}+3z^{4}a^{-6}-13z^{4}+3a^{5}z^{3}+5a^{3}z^{3}-5az^{3}-15z^{3}a^{-1}-10z^{3}a^{-3}-2z^{3}a^{-5}-a^{4}z^{2}-6a^{2}z^{2}-6z^{2}a^{-2}-z^{2}a^{-4}-10z^{2}-2a^{3}z-4az-4za^{-1}-2za^{-3}+2a^{2}+2a^{-2}+5$

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