K12a571

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a571

Polynomial invariants

Jones polynomial	$q^{9}-6q^{8}+15q^{7}-26q^{6}+36q^{5}-43q^{4}+45q^{3}-40q^{2}+32q-20+10q^{-1}-4q^{-2}+q^{-3}$
Alexander polynomial	$-2t^{4}+12t^{3}-33t^{2}+58t-69+58t^{-1}-33t^{-2}+12t^{-3}-2t^{-4}$
Conway polynomial	$-2z^{8}-4z^{6}-z^{4}+2z^{2}+1$
Determinant	279
Signature	2
HOMFLY-PT polynomial	$-z^{8}a^{-2}-z^{8}a^{-4}-4z^{6}a^{-2}-2z^{6}a^{-4}+z^{6}a^{-6}+z^{6}-8z^{4}a^{-2}+3z^{4}a^{-4}+z^{4}a^{-6}+3z^{4}-8z^{2}a^{-2}+9z^{2}a^{-4}-2z^{2}a^{-6}+3z^{2}-2a^{-2}+4a^{-4}-2a^{-6}+1$
Kauffman polynomial	$4z^{11}a^{-3}+4z^{11}a^{-5}+10z^{10}a^{-2}+24z^{10}a^{-4}+14z^{10}a^{-6}+11z^{9}a^{-1}+21z^{9}a^{-3}+30z^{9}a^{-5}+20z^{9}a^{-7}-6z^{8}a^{-2}-35z^{8}a^{-4}-6z^{8}a^{-6}+15z^{8}a^{-8}+8z^{8}+4az^{7}-16z^{7}a^{-1}-59z^{7}a^{-3}-79z^{7}a^{-5}-34z^{7}a^{-7}+6z^{7}a^{-9}+a^{2}z^{6}-15z^{6}a^{-2}-4z^{6}a^{-4}-29z^{6}a^{-6}-24z^{6}a^{-8}+z^{6}a^{-10}-14z^{6}-8az^{5}+6z^{5}a^{-1}+50z^{5}a^{-3}+54z^{5}a^{-5}+12z^{5}a^{-7}-6z^{5}a^{-9}-2a^{2}z^{4}+27z^{4}a^{-2}+29z^{4}a^{-4}+20z^{4}a^{-6}+7z^{4}a^{-8}+9z^{4}+5az^{3}+3z^{3}a^{-1}-10z^{3}a^{-3}-10z^{3}a^{-5}-2z^{3}a^{-7}+a^{2}z^{2}-15z^{2}a^{-2}-17z^{2}a^{-4}-6z^{2}a^{-6}+z^{2}a^{-8}-4z^{2}-az-2za^{-1}-za^{-3}-za^{-5}+za^{-9}+2a^{-2}+4a^{-4}+2a^{-6}+1$

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