K12n683
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ - q^{-1} +4 q^{-2} -7 q^{-3} +12 q^{-4} -14 q^{-5} +15 q^{-6} -14 q^{-7} +11 q^{-8} -7 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+11 t^2-18 t+21-18 t^{-1} +11 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+7 z^4+6 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-6 z^2 a^8-3 a^8+z^8 a^6+6 z^6 a^6+14 z^4 a^6+14 z^2 a^6+4 a^6-z^6 a^4-3 z^4 a^4-2 z^2 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-5 z^4 a^{12}+2 z^2 a^{12}+5 z^7 a^{11}-8 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+5 z^8 a^{10}-6 z^6 a^{10}+2 z^4 a^{10}-z^2 a^{10}+3 z^9 a^9-2 z^5 a^9-2 z^3 a^9+2 z a^9+z^{10} a^8+3 z^8 a^8+z^6 a^8-11 z^4 a^8+10 z^2 a^8-3 a^8+4 z^9 a^7-6 z^7 a^7+12 z^5 a^7-16 z^3 a^7+6 z a^7+z^{10} a^6-2 z^8 a^6+14 z^6 a^6-26 z^4 a^6+17 z^2 a^6-4 a^6+z^9 a^5-z^7 a^5+6 z^5 a^5-10 z^3 a^5+3 z a^5+4 z^6 a^4-8 z^4 a^4+4 z^2 a^4+z^5 a^3-2 z^3 a^3+z a^3 }[/math] |
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