K12n747
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ - q^{-1} +5 q^{-2} -8 q^{-3} +13 q^{-4} -16 q^{-5} +17 q^{-6} -16 q^{-7} +12 q^{-8} -8 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+13 t^2-20 t+23-20 t^{-1} +13 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+3 z^4+3 z^2+1 }[/math] |
| Determinant | 101 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-2 z^2 a^8+z^8 a^6+5 z^6 a^6+8 z^4 a^6+3 z^2 a^6-2 a^6-z^6 a^4-2 z^4 a^4+2 z^2 a^4+3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-6 z^4 a^{12}+z^2 a^{12}+7 z^7 a^{11}-12 z^5 a^{11}+5 z^3 a^{11}-z a^{11}+7 z^8 a^{10}-10 z^6 a^{10}+3 z^4 a^{10}+4 z^9 a^9+z^7 a^9-12 z^5 a^9+11 z^3 a^9-2 z a^9+z^{10} a^8+8 z^8 a^8-16 z^6 a^8+9 z^4 a^8+z^2 a^8+5 z^9 a^7-4 z^7 a^7-4 z^5 a^7+8 z^3 a^7-4 z a^7+z^{10} a^6+z^8 a^6+3 z^6 a^6-8 z^4 a^6+z^2 a^6+2 a^6+z^9 a^5+2 z^7 a^5-4 z^5 a^5+2 z^3 a^5-3 z a^5+5 z^6 a^4-8 z^4 a^4-z^2 a^4+3 a^4+z^5 a^3-z^3 a^3 }[/math] |
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