K12a969
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+7 q^5-12 q^4+17 q^3-20 q^2+21 q-20+16 q^{-1} -11 q^{-2} +7 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-14 t^2+33 t-41+33 t^{-1} -14 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-2 z^4-5 z^2+1 }[/math] |
| Determinant | 139 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-2 a^2 z^4+z^4 a^{-2} -2 z^4 a^{-4} +z^4+a^4 z^2-3 a^2 z^2-3 z^2 a^{-4} +z^2 a^{-6} -z^2+a^4+ a^{-2} - a^{-4} + a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+6 z^{10} a^{-2} +10 z^{10}+3 a^3 z^9+6 z^9 a^{-1} +9 z^9 a^{-3} +a^4 z^8-16 a^2 z^8-10 z^8 a^{-2} +10 z^8 a^{-4} -37 z^8-14 a^3 z^7-25 a z^7-37 z^7 a^{-1} -17 z^7 a^{-3} +9 z^7 a^{-5} -5 a^4 z^6+16 a^2 z^6-z^6 a^{-2} -16 z^6 a^{-4} +6 z^6 a^{-6} +42 z^6+20 a^3 z^5+42 a z^5+47 z^5 a^{-1} +9 z^5 a^{-3} -13 z^5 a^{-5} +3 z^5 a^{-7} +8 a^4 z^4-a^2 z^4+6 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} -22 z^4-10 a^3 z^3-22 a z^3-29 z^3 a^{-1} -6 z^3 a^{-3} +9 z^3 a^{-5} -2 z^3 a^{-7} -5 a^4 z^2-a^2 z^2+z^2 a^{-2} +3 z^2 a^{-4} +4 z^2 a^{-6} -z^2 a^{-8} +7 z^2+2 a^3 z+4 a z+6 z a^{-1} +3 z a^{-3} -z a^{-5} +a^4- a^{-2} - a^{-4} - a^{-6} -1 }[/math] |
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