K12a1210

Symmetrical form

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{2}-4q+8-13q^{-1}+20q^{-2}-23q^{-3}+25q^{-4}-24q^{-5}+20q^{-6}-14q^{-7}+8q^{-8}-4q^{-9}+q^{-10}$
Alexander polynomial	$-t^{5}+5t^{4}-12t^{3}+21t^{2}-28t+31-28t^{-1}+21t^{-2}-12t^{-3}+5t^{-4}-t^{-5}$
Conway polynomial	$-z^{10}-5z^{8}-7z^{6}-z^{4}+3z^{2}+1$
Determinant	165
Signature	-4
HOMFLY-PT polynomial	$-a^{4}z^{10}+a^{6}z^{8}-7a^{4}z^{8}+a^{2}z^{8}+5a^{6}z^{6}-17a^{4}z^{6}+5a^{2}z^{6}+7a^{6}z^{4}-15a^{4}z^{4}+7a^{2}z^{4}+a^{6}z^{2}+2a^{2}z^{2}-2a^{6}+3a^{4}$
Kauffman polynomial	$z^{4}a^{12}+4z^{5}a^{11}-2z^{3}a^{11}+8z^{6}a^{10}-6z^{4}a^{10}+z^{2}a^{10}+12z^{7}a^{9}-14z^{5}a^{9}+4z^{3}a^{9}+14z^{8}a^{8}-22z^{6}a^{8}+7z^{4}a^{8}+2z^{2}a^{8}+12z^{9}a^{7}-18z^{7}a^{7}-6z^{5}a^{7}+14z^{3}a^{7}-4za^{7}+8z^{10}a^{6}-11z^{8}a^{6}-8z^{6}a^{6}+5z^{4}a^{6}+2a^{6}+3z^{11}a^{5}+5z^{9}a^{5}-33z^{7}a^{5}+23z^{5}a^{5}+4z^{3}a^{5}-5za^{5}+14z^{10}a^{4}-53z^{8}a^{4}+66z^{6}a^{4}-36z^{4}a^{4}+3z^{2}a^{4}+3a^{4}+3z^{11}a^{3}-3z^{9}a^{3}-21z^{7}a^{3}+35z^{5}a^{3}-12z^{3}a^{3}-za^{3}+6z^{10}a^{2}-27z^{8}a^{2}+40z^{6}a^{2}-23z^{4}a^{2}+4z^{2}a^{2}+4z^{9}a-18z^{7}a+24z^{5}a-8z^{3}a+z^{8}-4z^{6}+4z^{4}$