K12a123

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{2}-3q+7-12q^{-1}+18q^{-2}-21q^{-3}+23q^{-4}-22q^{-5}+18q^{-6}-13q^{-7}+7q^{-8}-3q^{-9}+q^{-10}$
Alexander polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^4-7 t^3+19 t^2-30 t+35-30 t^{-1} +19 t^{-2} -7 t^{-3} + t^{-4} }
Conway polynomial	$z^{8}+z^{6}-3z^{4}-z^{2}+1$
Determinant	149
Signature	-4
HOMFLY-PT polynomial	$z^{4}a^{8}+3z^{2}a^{8}+2a^{8}-2z^{6}a^{6}-8z^{4}a^{6}-11z^{2}a^{6}-6a^{6}+z^{8}a^{4}+5z^{6}a^{4}+11z^{4}a^{4}+14z^{2}a^{4}+7a^{4}-2z^{6}a^{2}-8z^{4}a^{2}-10z^{2}a^{2}-4a^{2}+z^{4}+3z^{2}+2$
Kauffman polynomial	$z^{4}a^{12}-z^{2}a^{12}+3z^{5}a^{11}-2z^{3}a^{11}+6z^{6}a^{10}-5z^{4}a^{10}+2z^{2}a^{10}+10z^{7}a^{9}-16z^{5}a^{9}+14z^{3}a^{9}-4za^{9}+12z^{8}a^{8}-23z^{6}a^{8}+18z^{4}a^{8}-7z^{2}a^{8}+2a^{8}+10z^{9}a^{7}-15z^{7}a^{7}-6z^{5}a^{7}+15z^{3}a^{7}-6za^{7}+5z^{10}a^{6}+5z^{8}a^{6}-48z^{6}a^{6}+56z^{4}a^{6}-28z^{2}a^{6}+6a^{6}+z^{11}a^{5}+16z^{9}a^{5}-59z^{7}a^{5}+56z^{5}a^{5}-19z^{3}a^{5}+za^{5}+8z^{10}a^{4}-15z^{8}a^{4}-23z^{6}a^{4}+54z^{4}a^{4}-32z^{2}a^{4}+7a^{4}+z^{11}a^{3}+9z^{9}a^{3}-48z^{7}a^{3}+65z^{5}a^{3}-31z^{3}a^{3}+5za^{3}+3z^{10}a^{2}-7z^{8}a^{2}-9z^{6}a^{2}+31z^{4}a^{2}-21z^{2}a^{2}+4a^{2}+3z^{9}a-14z^{7}a+22z^{5}a-13z^{3}a+2za+z^{8}-5z^{6}+9z^{4}-7z^{2}+2$