K13n856

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13n856

Polynomial invariants

Jones polynomial	Data:K13n856/Jones Polynomial
Alexander polynomial	$-t^{4}+3t^{3}-6t^{2}+12t-15+12t^{-1}-6t^{-2}+3t^{-3}-t^{-4}$
Conway polynomial	Data:K13n856/Conway Polynomial
Determinant	59
Signature	2
HOMFLY-PT polynomial	$-z^{8}a^{-2}-6z^{6}a^{-2}+z^{6}-13z^{4}a^{-2}-z^{4}a^{-4}+2z^{4}a^{-6}+4z^{4}-11z^{2}a^{-2}-2z^{2}a^{-4}+7z^{2}a^{-6}-z^{2}a^{-8}+6z^{2}-3a^{-2}-2a^{-4}+5a^{-6}-2a^{-8}+3$
Kauffman polynomial	$z^{11}a^{-5}+z^{11}a^{-7}+z^{10}a^{-2}+2z^{10}a^{-4}+3z^{10}a^{-6}+2z^{10}a^{-8}+4z^{9}a^{-1}+4z^{9}a^{-3}-7z^{9}a^{-5}-6z^{9}a^{-7}+z^{9}a^{-9}+4z^{8}a^{-2}-13z^{8}a^{-4}-27z^{8}a^{-6}-15z^{8}a^{-8}+5z^{8}+3az^{7}-10z^{7}a^{-1}-13z^{7}a^{-3}+10z^{7}a^{-5}+3z^{7}a^{-7}-7z^{7}a^{-9}+a^{2}z^{6}-20z^{6}a^{-2}+33z^{6}a^{-4}+72z^{6}a^{-6}+35z^{6}a^{-8}-15z^{6}-8az^{5}+7z^{5}a^{-1}+18z^{5}a^{-3}+8z^{5}a^{-5}+20z^{5}a^{-7}+15z^{5}a^{-9}-3a^{2}z^{4}+26z^{4}a^{-2}-31z^{4}a^{-4}-73z^{4}a^{-6}-33z^{4}a^{-8}+14z^{4}+4az^{3}-7z^{3}a^{-1}-10z^{3}a^{-3}-10z^{3}a^{-5}-23z^{3}a^{-7}-12z^{3}a^{-9}+2a^{2}z^{2}-17z^{2}a^{-2}+15z^{2}a^{-4}+33z^{2}a^{-6}+13z^{2}a^{-8}-10z^{2}+2za^{-1}+2za^{-3}+2za^{-5}+5za^{-7}+3za^{-9}+3a^{-2}-2a^{-4}-5a^{-6}-2a^{-8}+3$

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