K12a836
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+12 q^2-16 q+19-19 q^{-1} +18 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^2-24 t+29-24 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+5 z^2+1 }[/math] |
| Determinant | 125 |
| 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} +3 z^2-4 a^4+7 a^2- a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+6 a^2 z^{10}+4 z^{10}+2 a^5 z^9+a^3 z^9+6 a z^9+7 z^9 a^{-1} +2 a^6 z^8-5 a^4 z^8-22 a^2 z^8+8 z^8 a^{-2} -7 z^8+a^7 z^7-4 a^5 z^7-7 a^3 z^7-26 a z^7-18 z^7 a^{-1} +6 z^7 a^{-3} -8 a^6 z^6+9 a^4 z^6+47 a^2 z^6-21 z^6 a^{-2} +3 z^6 a^{-4} +6 z^6-5 a^7 z^5-4 a^5 z^5+13 a^3 z^5+48 a z^5+22 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4-21 a^4 z^4-57 a^2 z^4+24 z^4 a^{-2} -5 z^4 a^{-4} +2 z^4+8 a^7 z^3+9 a^5 z^3-20 a^3 z^3-39 a z^3-7 z^3 a^{-1} +9 z^3 a^{-3} -2 z^3 a^{-5} -2 a^6 z^2+18 a^4 z^2+29 a^2 z^2-9 z^2 a^{-2} -4 a^7 z-2 a^5 z+8 a^3 z+9 a z+z a^{-1} -2 z a^{-3} -4 a^4-7 a^2+ a^{-2} -1 }[/math] |
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