K12a1137

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1137

Polynomial invariants

Jones polynomial	$q^{8}-2q^{7}+5q^{6}-10q^{5}+14q^{4}-19q^{3}+22q^{2}-21q+19-14q^{-1}+9q^{-2}-4q^{-3}+q^{-4}$
Alexander polynomial	$-4t^{3}+16t^{2}-31t+39-31t^{-1}+16t^{-2}-4t^{-3}$
Conway polynomial	$-4z^{6}-8z^{4}-3z^{2}+1$
Determinant	141
Signature	0
HOMFLY-PT polynomial	$-2z^{6}a^{-2}-z^{6}a^{-4}-z^{6}+a^{2}z^{4}-6z^{4}a^{-2}-3z^{4}a^{-4}+z^{4}a^{-6}-z^{4}+a^{2}z^{2}-5z^{2}a^{-2}-4z^{2}a^{-4}+3z^{2}a^{-6}+2z^{2}-3a^{-4}+2a^{-6}+2$
Kauffman polynomial	$z^{11}a^{-3}+z^{11}a^{-5}+4z^{10}a^{-2}+6z^{10}a^{-4}+2z^{10}a^{-6}+9z^{9}a^{-1}+9z^{9}a^{-3}+2z^{9}a^{-5}+2z^{9}a^{-7}+5z^{8}a^{-2}-15z^{8}a^{-4}-6z^{8}a^{-6}+z^{8}a^{-8}+13z^{8}+13az^{7}-9z^{7}a^{-1}-28z^{7}a^{-3}-16z^{7}a^{-5}-10z^{7}a^{-7}+9a^{2}z^{6}-29z^{6}a^{-2}+6z^{6}a^{-4}+z^{6}a^{-6}-6z^{6}a^{-8}-19z^{6}+4a^{3}z^{5}-17az^{5}-6z^{5}a^{-1}+17z^{5}a^{-3}+19z^{5}a^{-5}+17z^{5}a^{-7}+a^{4}z^{4}-8a^{2}z^{4}+21z^{4}a^{-2}-z^{4}a^{-4}+7z^{4}a^{-6}+12z^{4}a^{-8}+8z^{4}-a^{3}z^{3}+7az^{3}+z^{3}a^{-1}-3z^{3}a^{-3}-8z^{3}a^{-5}-12z^{3}a^{-7}+3a^{2}z^{2}-7z^{2}a^{-2}+7z^{2}a^{-4}-z^{2}a^{-6}-8z^{2}a^{-8}-4z^{2}+za^{-3}+5za^{-5}+4za^{-7}-3a^{-4}-2a^{-6}+2$

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