K12a991

Two figure 8 knots on a loop, doubly interlinked.

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{2}-4q+10-17q^{-1}+25q^{-2}-30q^{-3}+33q^{-4}-31q^{-5}+25q^{-6}-18q^{-7}+10q^{-8}-4q^{-9}+q^{-10}$
Alexander polynomial	$t^{4}-8t^{3}+25t^{2}-44t+53-44t^{-1}+25t^{-2}-8t^{-3}+t^{-4}$
Conway polynomial	$z^{8}-3z^{4}+1$
Determinant	209
Signature	-4
HOMFLY-PT polynomial	$z^{4}a^{8}+2z^{2}a^{8}+a^{8}-2z^{6}a^{6}-6z^{4}a^{6}-6z^{2}a^{6}-3a^{6}+z^{8}a^{4}+4z^{6}a^{4}+7z^{4}a^{4}+7z^{2}a^{4}+3a^{4}-2z^{6}a^{2}-6z^{4}a^{2}-5z^{2}a^{2}-a^{2}+z^{4}+2z^{2}+1$
Kauffman polynomial	$z^{4}a^{12}+4z^{5}a^{11}+10z^{6}a^{10}-6z^{4}a^{10}+2z^{2}a^{10}+18z^{7}a^{9}-24z^{5}a^{9}+12z^{3}a^{9}-2za^{9}+23z^{8}a^{8}-41z^{6}a^{8}+22z^{4}a^{8}-6z^{2}a^{8}+a^{8}+21z^{9}a^{7}-39z^{7}a^{7}+12z^{5}a^{7}+z^{3}a^{7}-2za^{7}+12z^{10}a^{6}-7z^{8}a^{6}-47z^{6}a^{6}+51z^{4}a^{6}-19z^{2}a^{6}+3a^{6}+3z^{11}a^{5}+24z^{9}a^{5}-99z^{7}a^{5}+100z^{5}a^{5}-36z^{3}a^{5}+4za^{5}+18z^{10}a^{4}-50z^{8}a^{4}+19z^{6}a^{4}+28z^{4}a^{4}-17z^{2}a^{4}+3a^{4}+3z^{11}a^{3}+7z^{9}a^{3}-58z^{7}a^{3}+82z^{5}a^{3}-37z^{3}a^{3}+6za^{3}+6z^{10}a^{2}-19z^{8}a^{2}+11z^{6}a^{2}+12z^{4}a^{2}-10z^{2}a^{2}+a^{2}+4z^{9}a-16z^{7}a+22z^{5}a-12z^{3}a+2za+z^{8}-4z^{6}+6z^{4}-4z^{2}+1$