K12a982
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+17 q^2-24 q+29-29 q^{-1} +28 q^{-2} -21 q^{-3} +14 q^{-4} -8 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+23 t^2-38 t+45-38 t^{-1} +23 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+9 z^4+5 z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+5 a^2 z^6-z^6 a^{-2} +4 z^6-4 a^4 z^4+11 a^2 z^4-3 z^4 a^{-2} +5 z^4-6 a^4 z^2+13 a^2 z^2-3 z^2 a^{-2} +z^2-4 a^4+7 a^2- a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+12 a^2 z^{10}+7 z^{10}+5 a^5 z^9+7 a^3 z^9+14 a z^9+12 z^9 a^{-1} +3 a^6 z^8-12 a^4 z^8-29 a^2 z^8+13 z^8 a^{-2} -z^8+a^7 z^7-15 a^5 z^7-32 a^3 z^7-43 a z^7-18 z^7 a^{-1} +9 z^7 a^{-3} -10 a^6 z^6+12 a^4 z^6+33 a^2 z^6-23 z^6 a^{-2} +4 z^6 a^{-4} -16 z^6-4 a^7 z^5+14 a^5 z^5+45 a^3 z^5+50 a z^5+9 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4-15 a^4 z^4-31 a^2 z^4+18 z^4 a^{-2} -4 z^4 a^{-4} +15 z^4+5 a^7 z^3-7 a^5 z^3-39 a^3 z^3-35 a z^3+7 z^3 a^{-3} -z^3 a^{-5} -a^6 z^2+12 a^4 z^2+17 a^2 z^2-6 z^2 a^{-2} -2 z^2-2 a^7 z+4 a^5 z+14 a^3 z+11 a z+z a^{-1} -2 z a^{-3} -4 a^4-7 a^2+ a^{-2} -1 }[/math] |
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