K12a1112

Knot presentations

Dowker-Thistlethwaite code

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

Polynomial invariants

Jones polynomial	$q^{15}-4q^{14}+9q^{13}-17q^{12}+25q^{11}-32q^{10}+34q^{9}-32q^{8}+27q^{7}-18q^{6}+11q^{5}-4q^{4}+q^{3}$
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 8 t^3-27 t^2+46 t-53+46 t^{-1} -27 t^{-2} +8 t^{-3} }
Conway polynomial	$8z^{6}+21z^{4}+10z^{2}+1$
Determinant	215
Signature	6
HOMFLY-PT polynomial	$z^{6}a^{-6}+4z^{6}a^{-8}+3z^{6}a^{-10}+2z^{4}a^{-6}+14z^{4}a^{-8}+9z^{4}a^{-10}-4z^{4}a^{-12}+13z^{2}a^{-8}+7z^{2}a^{-10}-11z^{2}a^{-12}+z^{2}a^{-14}+3a^{-8}+2a^{-10}-6a^{-12}+2a^{-14}$
Kauffman polynomial	$3z^{11}a^{-11}+3z^{11}a^{-13}+10z^{10}a^{-10}+17z^{10}a^{-12}+7z^{10}a^{-14}+13z^{9}a^{-9}+15z^{9}a^{-11}+10z^{9}a^{-13}+8z^{9}a^{-15}+10z^{8}a^{-8}-19z^{8}a^{-10}-43z^{8}a^{-12}-7z^{8}a^{-14}+7z^{8}a^{-16}+4z^{7}a^{-7}-33z^{7}a^{-9}-58z^{7}a^{-11}-35z^{7}a^{-13}-10z^{7}a^{-15}+4z^{7}a^{-17}+z^{6}a^{-6}-26z^{6}a^{-8}+12z^{6}a^{-10}+54z^{6}a^{-12}+z^{6}a^{-14}-13z^{6}a^{-16}+z^{6}a^{-18}-7z^{5}a^{-7}+28z^{5}a^{-9}+75z^{5}a^{-11}+46z^{5}a^{-13}-3z^{5}a^{-15}-9z^{5}a^{-17}-2z^{4}a^{-6}+24z^{4}a^{-8}-4z^{4}a^{-10}-41z^{4}a^{-12}-4z^{4}a^{-14}+5z^{4}a^{-16}-2z^{4}a^{-18}-6z^{3}a^{-9}-38z^{3}a^{-11}-33z^{3}a^{-13}+5z^{3}a^{-15}+6z^{3}a^{-17}-13z^{2}a^{-8}+6z^{2}a^{-10}+22z^{2}a^{-12}+3z^{2}a^{-14}+z^{2}a^{-16}+z^{2}a^{-18}-2za^{-9}+7za^{-11}+9za^{-13}-za^{-15}-za^{-17}+3a^{-8}-2a^{-10}-6a^{-12}-2a^{-14}$