K12a477

Knotscape

Symmetrical representation as decorative knot

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{6}-3q^{5}+8q^{4}-14q^{3}+20q^{2}-25q+27-25q^{-1}+20q^{-2}-14q^{-3}+8q^{-4}-3q^{-5}+q^{-6}$
Alexander polynomial	$-t^{3}+11t^{2}-41t+63-41t^{-1}+11t^{-2}-t^{-3}$
Conway polynomial	$-z^{6}+5z^{4}-6z^{2}+1$
Determinant	169
Signature	0
HOMFLY-PT polynomial	$a^{6}-3z^{2}a^{4}-a^{4}+3z^{4}a^{2}+2z^{2}a^{2}+a^{2}-z^{6}-z^{4}-4z^{2}-1+3z^{4}a^{-2}+2z^{2}a^{-2}+a^{-2}-3z^{2}a^{-4}-a^{-4}+a^{-6}$
Kauffman polynomial	$az^{11}+z^{11}a^{-1}+3a^{2}z^{10}+3z^{10}a^{-2}+6z^{10}+5a^{3}z^{9}+8az^{9}+8z^{9}a^{-1}+5z^{9}a^{-3}+5a^{4}z^{8}+5a^{2}z^{8}+5z^{8}a^{-2}+5z^{8}a^{-4}+3a^{5}z^{7}-4a^{3}z^{7}-7az^{7}-7z^{7}a^{-1}-4z^{7}a^{-3}+3z^{7}a^{-5}+a^{6}z^{6}-9a^{4}z^{6}-14a^{2}z^{6}-14z^{6}a^{-2}-9z^{6}a^{-4}+z^{6}a^{-6}-8z^{6}-7a^{5}z^{5}-5a^{3}z^{5}-9az^{5}-9z^{5}a^{-1}-5z^{5}a^{-3}-7z^{5}a^{-5}-3a^{6}z^{4}+3a^{4}z^{4}+5a^{2}z^{4}+5z^{4}a^{-2}+3z^{4}a^{-4}-3z^{4}a^{-6}-2z^{4}+5a^{5}z^{3}+4a^{3}z^{3}+8az^{3}+8z^{3}a^{-1}+4z^{3}a^{-3}+5z^{3}a^{-5}+3a^{6}z^{2}+2a^{4}z^{2}+2a^{2}z^{2}+2z^{2}a^{-2}+2z^{2}a^{-4}+3z^{2}a^{-6}+6z^{2}-a^{5}z-az-za^{-1}-za^{-5}-a^{6}-a^{4}-a^{2}-a^{-2}-a^{-4}-a^{-6}-1$