K12a186
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+5-10 q^{-1} +17 q^{-2} -24 q^{-3} +29 q^{-4} -30 q^{-5} +28 q^{-6} -22 q^{-7} +15 q^{-8} -8 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+25 t^2-40 t+45-40 t^{-1} +25 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-3 z^4+4 z^2+1 }[/math] |
| Determinant | 193 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-2 a^{10}+3 z^4 a^8+8 z^2 a^8+4 a^8-3 z^6 a^6-10 z^4 a^6-9 z^2 a^6-3 a^6+z^8 a^4+4 z^6 a^4+6 z^4 a^4+5 z^2 a^4+a^4-z^6 a^2-2 z^4 a^2+z^2 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-8 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+9 z^8 a^{10}-15 z^6 a^{10}+16 z^4 a^{10}-9 z^2 a^{10}+2 a^{10}+9 z^9 a^9-11 z^7 a^9+3 z^5 a^9+5 z^3 a^9-2 z a^9+6 z^{10} a^8+2 z^8 a^8-26 z^6 a^8+35 z^4 a^8-19 z^2 a^8+4 a^8+2 z^{11} a^7+15 z^9 a^7-47 z^7 a^7+46 z^5 a^7-19 z^3 a^7+2 z a^7+13 z^{10} a^6-24 z^8 a^6-4 z^6 a^6+26 z^4 a^6-17 z^2 a^6+3 a^6+2 z^{11} a^5+15 z^9 a^5-60 z^7 a^5+62 z^5 a^5-23 z^3 a^5+z a^5+7 z^{10} a^4-12 z^8 a^4-11 z^6 a^4+21 z^4 a^4-7 z^2 a^4+a^4+9 z^9 a^3-29 z^7 a^3+26 z^5 a^3-6 z^3 a^3+5 z^8 a^2-15 z^6 a^2+10 z^4 a^2+z^2 a^2-a^2+z^7 a-2 z^5 a }[/math] |
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