K12n852
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+6 q^4-11 q^3+17 q^2-20 q+21-19 q^{-1} +15 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+14 t^2-26 t+33-26 t^{-1} +14 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+4 z^4+z^2+1 }[/math] |
| Determinant | 125 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +5 z^6-3 a^2 z^4-2 z^4 a^{-2} +9 z^4-3 a^2 z^2-z^2 a^{-4} +5 z^2+2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+7 a z^9+10 z^9 a^{-1} +3 z^9 a^{-3} +10 a^2 z^8+2 z^8 a^{-2} +z^8 a^{-4} +11 z^8+8 a^3 z^7-6 a z^7-18 z^7 a^{-1} -4 z^7 a^{-3} +4 a^4 z^6-17 a^2 z^6-4 z^6 a^{-2} +4 z^6 a^{-4} -29 z^6+a^5 z^5-12 a^3 z^5-4 a z^5+12 z^5 a^{-1} +6 z^5 a^{-3} +3 z^5 a^{-5} -5 a^4 z^4+11 a^2 z^4-3 z^4 a^{-2} -11 z^4 a^{-4} +24 z^4-a^5 z^3+5 a^3 z^3+6 a z^3-3 z^3 a^{-1} -9 z^3 a^{-3} -6 z^3 a^{-5} +a^4 z^2-4 a^2 z^2+5 z^2 a^{-2} +6 z^2 a^{-4} -6 z^2-a^3 z-2 a z+3 z a^{-3} +2 z a^{-5} -2 a^{-2} - a^{-4} }[/math] |
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