K12a5

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a5

Polynomial invariants

Jones polynomial	$q^{9}-4q^{8}+10q^{7}-18q^{6}+25q^{5}-30q^{4}+32q^{3}-29q^{2}+23q-15+8q^{-1}-3q^{-2}+q^{-3}$
Alexander polynomial	$3t^{3}-19t^{2}+47t-61+47t^{-1}-19t^{-2}+3t^{-3}$
Conway polynomial	$3z^{6}-z^{4}-2z^{2}+1$
Determinant	199
Signature	2
HOMFLY-PT polynomial	$z^{6}a^{-2}+2z^{6}a^{-4}-z^{4}a^{-2}+5z^{4}a^{-4}-3z^{4}a^{-6}-2z^{4}+a^{2}z^{2}-4z^{2}a^{-2}+7z^{2}a^{-4}-5z^{2}a^{-6}+z^{2}a^{-8}-2z^{2}+a^{2}-2a^{-2}+4a^{-4}-3a^{-6}+a^{-8}$
Kauffman polynomial	$z^{11}a^{-3}+z^{11}a^{-5}+4z^{10}a^{-2}+9z^{10}a^{-4}+5z^{10}a^{-6}+6z^{9}a^{-1}+17z^{9}a^{-3}+20z^{9}a^{-5}+9z^{9}a^{-7}+6z^{8}a^{-2}+2z^{8}a^{-4}+9z^{8}a^{-6}+8z^{8}a^{-8}+5z^{8}+3az^{7}-7z^{7}a^{-1}-40z^{7}a^{-3}-47z^{7}a^{-5}-13z^{7}a^{-7}+4z^{7}a^{-9}+a^{2}z^{6}-25z^{6}a^{-2}-39z^{6}a^{-4}-40z^{6}a^{-6}-16z^{6}a^{-8}+z^{6}a^{-10}-8z^{6}-7az^{5}+z^{5}a^{-1}+37z^{5}a^{-3}+39z^{5}a^{-5}+2z^{5}a^{-7}-8z^{5}a^{-9}-3a^{2}z^{4}+27z^{4}a^{-2}+48z^{4}a^{-4}+39z^{4}a^{-6}+11z^{4}a^{-8}-2z^{4}a^{-10}+2z^{4}+5az^{3}-16z^{3}a^{-3}-16z^{3}a^{-5}+5z^{3}a^{-9}+3a^{2}z^{2}-13z^{2}a^{-2}-22z^{2}a^{-4}-17z^{2}a^{-6}-5z^{2}a^{-8}+z^{2}a^{-10}+z^{2}-az+3za^{-3}+3za^{-5}-za^{-9}-a^{2}+2a^{-2}+4a^{-4}+3a^{-6}+a^{-8}$

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