K12a1152
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+14 q^4-27 q^3+40 q^2-49 q+53-49 q^{-1} +40 q^{-2} -27 q^{-3} +14 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+34 t^2-72 t+93-72 t^{-1} +34 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-z^2+1 }[/math] |
| Determinant | 325 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-4 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +6 z^4+a^4 z^2-5 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +7 z^2+a^4-3 a^2-3 a^{-2} + a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a z^{11}+5 z^{11} a^{-1} +16 a^2 z^{10}+16 z^{10} a^{-2} +32 z^{10}+20 a^3 z^9+40 a z^9+40 z^9 a^{-1} +20 z^9 a^{-3} +13 a^4 z^8-6 a^2 z^8-6 z^8 a^{-2} +13 z^8 a^{-4} -38 z^8+5 a^5 z^7-35 a^3 z^7-109 a z^7-109 z^7 a^{-1} -35 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-21 a^4 z^6-35 a^2 z^6-35 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -26 z^6-6 a^5 z^5+26 a^3 z^5+93 a z^5+93 z^5 a^{-1} +26 z^5 a^{-3} -6 z^5 a^{-5} -a^6 z^4+15 a^4 z^4+38 a^2 z^4+38 z^4 a^{-2} +15 z^4 a^{-4} -z^4 a^{-6} +44 z^4+2 a^5 z^3-11 a^3 z^3-41 a z^3-41 z^3 a^{-1} -11 z^3 a^{-3} +2 z^3 a^{-5} -5 a^4 z^2-16 a^2 z^2-16 z^2 a^{-2} -5 z^2 a^{-4} -22 z^2+3 a^3 z+8 a z+8 z a^{-1} +3 z a^{-3} +a^4+3 a^2+3 a^{-2} + a^{-4} +5 }[/math] |
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