K13a1814

Knotscape

Symmetrical depiction as decorative knot

More squared symmetrical depiction.

Dowker-Thistlethwaite code

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

Jones polynomial	Data:K13a1814/Jones Polynomial
Alexander polynomial	$-t^{4}+9t^{3}-33t^{2}+67t-83+67t^{-1}-33t^{-2}+9t^{-3}-t^{-4}$
Conway polynomial	Data:K13a1814/Conway Polynomial
Determinant	303
Signature	2
HOMFLY-PT polynomial	$-z^{8}a^{-2}-4z^{6}a^{-2}+2z^{6}a^{-4}+3z^{6}-3a^{2}z^{4}-9z^{4}a^{-2}+5z^{4}a^{-4}-z^{4}a^{-6}+9z^{4}+a^{4}z^{2}-6a^{2}z^{2}-8z^{2}a^{-2}+4z^{2}a^{-4}-z^{2}a^{-6}+10z^{2}+a^{4}-3a^{2}-a^{-2}+4$
Kauffman polynomial	$z^{12}a^{-2}+z^{12}+4az^{11}+9z^{11}a^{-1}+5z^{11}a^{-3}+6a^{2}z^{10}+24z^{10}a^{-2}+12z^{10}a^{-4}+18z^{10}+4a^{3}z^{9}+5az^{9}+12z^{9}a^{-1}+29z^{9}a^{-3}+18z^{9}a^{-5}+a^{4}z^{8}-17a^{2}z^{8}-41z^{8}a^{-2}+11z^{8}a^{-4}+18z^{8}a^{-6}-52z^{8}-16a^{3}z^{7}-56az^{7}-100z^{7}a^{-1}-87z^{7}a^{-3}-15z^{7}a^{-5}+12z^{7}a^{-7}-4a^{4}z^{6}+6a^{2}z^{6}-30z^{6}a^{-2}-64z^{6}a^{-4}-23z^{6}a^{-6}+5z^{6}a^{-8}+16z^{6}+23a^{3}z^{5}+85az^{5}+120z^{5}a^{-1}+63z^{5}a^{-3}-9z^{5}a^{-5}-13z^{5}a^{-7}+z^{5}a^{-9}+6a^{4}z^{4}+18a^{2}z^{4}+68z^{4}a^{-2}+53z^{4}a^{-4}+12z^{4}a^{-6}-3z^{4}a^{-8}+42z^{4}-14a^{3}z^{3}-45az^{3}-50z^{3}a^{-1}-18z^{3}a^{-3}+6z^{3}a^{-5}+5z^{3}a^{-7}-4a^{4}z^{2}-16a^{2}z^{2}-27z^{2}a^{-2}-15z^{2}a^{-4}-4z^{2}a^{-6}-28z^{2}+3a^{3}z+8az+8za^{-1}+4za^{-3}+za^{-5}+a^{4}+3a^{2}+a^{-2}+4$