K13a1345

Knotscape

Symmetrical depiction as quasi-Celtic decorative knot

Rectangular quasi-Celtic decorative knot

Dowker-Thistlethwaite code

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

Jones polynomial	Data:K13a1345/Jones Polynomial
Alexander polynomial	$t^{4}-11t^{3}+48t^{2}-109t+143-109t^{-1}+48t^{-2}-11t^{-3}+t^{-4}$
Conway polynomial	Data:K13a1345/Conway Polynomial
Determinant	481
Signature	0
HOMFLY-PT polynomial	$z^{8}-3a^{2}z^{6}-2z^{6}a^{-2}+2z^{6}+3a^{4}z^{4}-4a^{2}z^{4}-2z^{4}a^{-2}+z^{4}a^{-4}+4z^{4}-a^{6}z^{2}+2a^{4}z^{2}-2a^{2}z^{2}-z^{2}a^{-2}+2z^{2}+1$
Kauffman polynomial	$4a^{2}z^{12}+4z^{12}+12a^{3}z^{11}+29az^{11}+17z^{11}a^{-1}+16a^{4}z^{10}+39a^{2}z^{10}+30z^{10}a^{-2}+53z^{10}+12a^{5}z^{9}+8a^{3}z^{9}-14az^{9}+19z^{9}a^{-1}+29z^{9}a^{-3}+5a^{6}z^{8}-25a^{4}z^{8}-93a^{2}z^{8}-38z^{8}a^{-2}+17z^{8}a^{-4}-118z^{8}+a^{7}z^{7}-27a^{5}z^{7}-66a^{3}z^{7}-77az^{7}-91z^{7}a^{-1}-46z^{7}a^{-3}+6z^{7}a^{-5}-11a^{6}z^{6}+2a^{4}z^{6}+51a^{2}z^{6}+3z^{6}a^{-2}-21z^{6}a^{-4}+z^{6}a^{-6}+63z^{6}-2a^{7}z^{5}+24a^{5}z^{5}+68a^{3}z^{5}+81az^{5}+67z^{5}a^{-1}+24z^{5}a^{-3}-4z^{5}a^{-5}+9a^{6}z^{4}+14a^{4}z^{4}+8z^{4}a^{-2}+7z^{4}a^{-4}-4z^{4}+a^{7}z^{3}-9a^{5}z^{3}-25a^{3}z^{3}-27az^{3}-15z^{3}a^{-1}-3z^{3}a^{-3}-3a^{6}z^{2}-5a^{4}z^{2}-3a^{2}z^{2}-2z^{2}a^{-2}-3z^{2}+a^{5}z+3a^{3}z+3az+za^{-1}+1$