K12a1019

Knotscape

Three-fold symmetrical representation

K12a1019 as a geodesic line of the oblate spheroid

Jones polynomial	$q^6-6 q^5+16 q^4-30 q^3+44 q^2-54 q+59-54 q^{-1} +44 q^{-2} -30 q^{-3} +16 q^{-4} -6 q^{-5} + q^{-6}$
Alexander polynomial	$t^4-10 t^3+39 t^2-80 t+101-80 t^{-1} +39 t^{-2} -10 t^{-3} + t^{-4}$
Conway polynomial	$z^8-2 z^6-z^4+2 z^2+1$
Determinant	361
Signature	0
HOMFLY-PT polynomial	$z^8-2 a^2 z^6-2 z^6 a^{-2} +2 z^6+a^4 z^4-2 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} +z^4+2 a^2 z^2+2 z^2 a^{-2} -2 z^2-a^4+2 a^2+2 a^{-2} - a^{-4} -1$
Kauffman polynomial	$8 a z^{11}+8 z^{11} a^{-1} +22 a^2 z^{10}+22 z^{10} a^{-2} +44 z^{10}+25 a^3 z^9+37 a z^9+37 z^9 a^{-1} +25 z^9 a^{-3} +16 a^4 z^8-23 a^2 z^8-23 z^8 a^{-2} +16 z^8 a^{-4} -78 z^8+6 a^5 z^7-42 a^3 z^7-108 a z^7-108 z^7 a^{-1} -42 z^7 a^{-3} +6 z^7 a^{-5} +a^6 z^6-22 a^4 z^6-8 a^2 z^6-8 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} +30 z^6-5 a^5 z^5+23 a^3 z^5+78 a z^5+78 z^5 a^{-1} +23 z^5 a^{-3} -5 z^5 a^{-5} +7 a^4 z^4+5 a^2 z^4+5 z^4 a^{-2} +7 z^4 a^{-4} -4 z^4-7 a^3 z^3-17 a z^3-17 z^3 a^{-1} -7 z^3 a^{-3} +a^4 z^2+5 a^2 z^2+5 z^2 a^{-2} +z^2 a^{-4} +8 z^2+a^5 z+a^3 z+z a^{-3} +z a^{-5} -a^4-2 a^2-2 a^{-2} - a^{-4} -1$