K12n291
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^2+5 q-9+14 q^{-1} -15 q^{-2} +17 q^{-3} -15 q^{-4} +11 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-11 t^2+22 t-27+22 t^{-1} -11 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+7 z^4+5 z^2+1 }[/math] |
| Determinant | 99 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+2 z^4 a^4-2 a^4+2 z^6 a^2+8 z^4 a^2+12 z^2 a^2+7 a^2-2 z^4-5 z^2-3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+3 a^5 z^9+5 a^3 z^9+2 a z^9+5 a^6 z^8+6 a^4 z^8+2 a^2 z^8+z^8+5 a^7 z^7+3 a^5 z^7-5 a^3 z^7-3 a z^7+3 a^8 z^6-5 a^6 z^6-8 a^4 z^6+2 a^2 z^6+2 z^6+a^9 z^5-8 a^7 z^5-11 a^5 z^5+4 a^3 z^5+9 a z^5+3 z^5 a^{-1} -5 a^8 z^4+a^6 z^4-a^4 z^4-15 a^2 z^4-8 z^4-2 a^9 z^3+5 a^7 z^3+8 a^5 z^3-10 a^3 z^3-18 a z^3-7 z^3 a^{-1} +2 a^8 z^2-a^6 z^2+5 a^4 z^2+15 a^2 z^2+7 z^2+a^9 z-2 a^7 z-a^5 z+7 a^3 z+9 a z+4 z a^{-1} +a^6-2 a^4-7 a^2-3 }[/math] |
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