K12a189
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-11 q^3+19 q^2-28 q+34-35 q^{-1} +33 q^{-2} -26 q^{-3} +18 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+26 t^2-48 t+59-48 t^{-1} +26 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^4+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-9 a^2 z^4-2 z^4 a^{-2} +6 z^4-a^6 z^2+6 a^4 z^2-7 a^2 z^2+2 z^2-a^6+2 a^4+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+14 a^2 z^{10}+8 z^{10}+7 a^5 z^9+17 a^3 z^9+24 a z^9+14 z^9 a^{-1} +4 a^6 z^8-4 a^4 z^8-13 a^2 z^8+15 z^8 a^{-2} +10 z^8+a^7 z^7-18 a^5 z^7-55 a^3 z^7-58 a z^7-11 z^7 a^{-1} +11 z^7 a^{-3} -12 a^6 z^6-24 a^4 z^6-35 a^2 z^6-18 z^6 a^{-2} +5 z^6 a^{-4} -46 z^6-3 a^7 z^5+12 a^5 z^5+44 a^3 z^5+31 a z^5-12 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+33 a^4 z^4+48 a^2 z^4+4 z^4 a^{-2} -4 z^4 a^{-4} +35 z^4+3 a^7 z^3-a^5 z^3-9 a^3 z^3+4 a z^3+13 z^3 a^{-1} +4 z^3 a^{-3} -5 a^6 z^2-15 a^4 z^2-16 a^2 z^2+z^2 a^{-2} -5 z^2-a^7 z-a^5 z-a^3 z-3 a z-2 z a^{-1} +a^6+2 a^4- a^{-2} -1 }[/math] |
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