K12n92
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+5 q^4-10 q^3+15 q^2-17 q+19-16 q^{-1} +13 q^{-2} -8 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+12 t^2-23 t+29-23 t^{-1} +12 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 109 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-3 z^4 a^{-2} +15 z^4-7 a^2 z^2-4 z^2 a^{-2} -z^2 a^{-4} +17 z^2-4 a^2-2 a^{-2} - a^{-4} +8 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+4 a z^9+6 z^9 a^{-1} +2 z^9 a^{-3} +7 a^2 z^8+5 z^8 a^{-2} +z^8 a^{-4} +11 z^8+6 a^3 z^7+4 a z^7-3 z^7 a^{-1} -z^7 a^{-3} +3 a^4 z^6-11 a^2 z^6-10 z^6 a^{-2} +2 z^6 a^{-4} -26 z^6+a^5 z^5-10 a^3 z^5-22 a z^5-12 z^5 a^{-1} +2 z^5 a^{-3} +3 z^5 a^{-5} -4 a^4 z^4+10 a^2 z^4+7 z^4 a^{-2} -6 z^4 a^{-4} +27 z^4-2 a^5 z^3+8 a^3 z^3+26 a z^3+16 z^3 a^{-1} -7 z^3 a^{-3} -7 z^3 a^{-5} +a^4 z^2-9 a^2 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} -19 z^2+a^5 z-4 a^3 z-11 a z-7 z a^{-1} +3 z a^{-3} +4 z a^{-5} +4 a^2+2 a^{-2} - a^{-4} +8 }[/math] |
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