K12a669
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+2 q^5-4 q^4+6 q^3-7 q^2+9 q-9+9 q^{-1} -7 q^{-2} +6 q^{-3} -4 q^{-4} +2 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-9 t^2+14 t-15+14 t^{-1} -9 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+9 z^4+5 z^2+1 }[/math] |
| Determinant | 67 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6+z^6 a^{-2} +z^6-a^4 z^4+4 a^2 z^4+4 z^4 a^{-2} -z^4 a^{-4} +3 z^4-3 a^4 z^2+5 a^2 z^2+5 z^2 a^{-2} -3 z^2 a^{-4} +z^2-2 a^4+3 a^2+3 a^{-2} -2 a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +5 z^{10} a^{-2} +2 z^{10} a^{-4} +3 z^{10}+4 a z^9+z^9 a^{-1} -2 z^9 a^{-3} +z^9 a^{-5} +4 a^2 z^8-28 z^8 a^{-2} -13 z^8 a^{-4} -11 z^8+4 a^3 z^7-13 a z^7-24 z^7 a^{-1} -14 z^7 a^{-3} -7 z^7 a^{-5} +4 a^4 z^6-8 a^2 z^6+49 z^6 a^{-2} +28 z^6 a^{-4} +9 z^6+3 a^5 z^5-6 a^3 z^5+10 a z^5+47 z^5 a^{-1} +45 z^5 a^{-3} +17 z^5 a^{-5} +2 a^6 z^4-6 a^4 z^4-3 a^2 z^4-33 z^4 a^{-2} -24 z^4 a^{-4} -4 z^4+a^7 z^3-2 a^5 z^3-a^3 z^3-5 a z^3-30 z^3 a^{-1} -40 z^3 a^{-3} -17 z^3 a^{-5} -a^6 z^2+5 a^4 z^2+7 a^2 z^2+12 z^2 a^{-2} +9 z^2 a^{-4} +4 z^2-a^7 z+a^5 z+2 a^3 z+a z+6 z a^{-1} +11 z a^{-3} +6 z a^{-5} -2 a^4-3 a^2-3 a^{-2} -2 a^{-4} -1 }[/math] |
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