K12a879
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+11 q^2-15 q+19-18 q^{-1} +17 q^{-2} -13 q^{-3} +9 q^{-4} -5 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+15 t^2-23 t+27-23 t^{-1} +15 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+13 z^4+6 z^2+1 }[/math] |
| Determinant | 121 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+6 a^2 z^6-z^6 a^{-2} +5 z^6-5 a^4 z^4+14 a^2 z^4-4 z^4 a^{-2} +8 z^4-8 a^4 z^2+15 a^2 z^2-5 z^2 a^{-2} +4 z^2-4 a^4+6 a^2-2 a^{-2} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+3 a^5 z^9+3 a^3 z^9+5 a z^9+5 z^9 a^{-1} +2 a^6 z^8-12 a^4 z^8-21 a^2 z^8+6 z^8 a^{-2} -z^8+a^7 z^7-12 a^5 z^7-22 a^3 z^7-21 a z^7-7 z^7 a^{-1} +5 z^7 a^{-3} -8 a^6 z^6+23 a^4 z^6+36 a^2 z^6-11 z^6 a^{-2} +3 z^6 a^{-4} -9 z^6-5 a^7 z^5+17 a^5 z^5+45 a^3 z^5+33 a z^5+z^5 a^{-1} -8 z^5 a^{-3} +z^5 a^{-5} +8 a^6 z^4-29 a^4 z^4-36 a^2 z^4+10 z^4 a^{-2} -5 z^4 a^{-4} +16 z^4+7 a^7 z^3-14 a^5 z^3-45 a^3 z^3-22 a z^3+7 z^3 a^{-1} +3 z^3 a^{-3} -2 z^3 a^{-5} -a^6 z^2+15 a^4 z^2+20 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} -4 z^2-2 a^7 z+5 a^5 z+14 a^3 z+7 a z-3 z a^{-1} -2 z a^{-3} +z a^{-5} -4 a^4-6 a^2+2 a^{-2} +1 }[/math] |
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