K12a1281
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+5 q^4-9 q^3+13 q^2-16 q+17-16 q^{-1} +13 q^{-2} -9 q^{-3} +5 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+13 t^2-23 t+29-23 t^{-1} +13 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-11 z^4-7 z^2+1 }[/math] |
| Determinant | 109 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-3 a^2 z^4-3 z^4 a^{-2} +z^4 a^{-4} -7 z^4+3 a^4 z^2-3 a^2 z^2-3 z^2 a^{-2} +3 z^2 a^{-4} -7 z^2+2 a^4-a^2- a^{-2} +2 a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+2 z^{10} a^{-2} +4 z^{10}+3 a^3 z^9-a z^9-z^9 a^{-1} +3 z^9 a^{-3} +3 a^4 z^8-3 a^2 z^8-3 z^8 a^{-2} +3 z^8 a^{-4} -12 z^8+2 a^5 z^7-8 a^3 z^7+7 a z^7+7 z^7 a^{-1} -8 z^7 a^{-3} +2 z^7 a^{-5} +a^6 z^6-9 a^4 z^6+3 a^2 z^6+3 z^6 a^{-2} -9 z^6 a^{-4} +z^6 a^{-6} +26 z^6-6 a^5 z^5+12 a^3 z^5-15 a z^5-15 z^5 a^{-1} +12 z^5 a^{-3} -6 z^5 a^{-5} -4 a^6 z^4+11 a^4 z^4+a^2 z^4+z^4 a^{-2} +11 z^4 a^{-4} -4 z^4 a^{-6} -28 z^4+4 a^5 z^3-11 a^3 z^3+15 a z^3+15 z^3 a^{-1} -11 z^3 a^{-3} +4 z^3 a^{-5} +4 a^6 z^2-9 a^4 z^2-5 a^2 z^2-5 z^2 a^{-2} -9 z^2 a^{-4} +4 z^2 a^{-6} +16 z^2+a^3 z-4 a z-4 z a^{-1} +z a^{-3} +2 a^4+a^2+ a^{-2} +2 a^{-4} -1 }[/math] |
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