K12a79
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-9 q^5+17 q^4-24 q^3+29 q^2-32 q+30-24 q^{-1} +17 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-43 t+55-43 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-2 z^2+1 }[/math] |
| Determinant | 201 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +5 z^6-3 a^2 z^4-11 z^4 a^{-2} +3 z^4 a^{-4} +11 z^4-3 a^2 z^2-15 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-6} +10 z^2-7 a^{-2} +5 a^{-4} - a^{-6} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +9 z^{10} a^{-2} +4 z^{10} a^{-4} +5 z^{10}+10 a z^9+22 z^9 a^{-1} +18 z^9 a^{-3} +6 z^9 a^{-5} +11 a^2 z^8+7 z^8 a^{-2} +6 z^8 a^{-4} +4 z^8 a^{-6} +16 z^8+8 a^3 z^7-6 a z^7-49 z^7 a^{-1} -50 z^7 a^{-3} -14 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-14 a^2 z^6-72 z^6 a^{-2} -47 z^6 a^{-4} -13 z^6 a^{-6} -56 z^6+a^5 z^5-10 a^3 z^5-9 a z^5+27 z^5 a^{-1} +33 z^5 a^{-3} +5 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4+8 a^2 z^4+89 z^4 a^{-2} +60 z^4 a^{-4} +15 z^4 a^{-6} +57 z^4-a^5 z^3+5 a^3 z^3+10 a z^3-3 z^3 a^{-1} -5 z^3 a^{-3} +5 z^3 a^{-5} +3 z^3 a^{-7} +2 a^4 z^2-2 a^2 z^2-44 z^2 a^{-2} -30 z^2 a^{-4} -7 z^2 a^{-6} -25 z^2-a^3 z-2 a z+z a^{-1} +z a^{-3} -2 z a^{-5} -z a^{-7} +7 a^{-2} +5 a^{-4} + a^{-6} +4 }[/math] |
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