K12a791
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+2 q^5-3 q^4+5 q^3-7 q^2+8 q-8+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+13 t-13+13 t^{-1} -9 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+9 z^4+4 z^2+1 }[/math] |
| Determinant | 63 |
| 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+4 z^2 a^{-2} -3 z^2 a^{-4} +z^2-2 a^4+3 a^2+ a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +4 z^{10} a^{-2} +2 z^{10} a^{-4} +2 z^{10}+3 a z^9-2 z^9 a^{-1} -4 z^9 a^{-3} +z^9 a^{-5} +4 a^2 z^8-23 z^8 a^{-2} -14 z^8 a^{-4} -5 z^8+4 a^3 z^7-7 a z^7-5 z^7 a^{-1} -z^7 a^{-3} -7 z^7 a^{-5} +4 a^4 z^6-9 a^2 z^6+43 z^6 a^{-2} +33 z^6 a^{-4} -3 z^6+3 a^5 z^5-6 a^3 z^5-2 a z^5+8 z^5 a^{-1} +17 z^5 a^{-3} +16 z^5 a^{-5} +2 a^6 z^4-6 a^4 z^4+a^2 z^4-32 z^4 a^{-2} -30 z^4 a^{-4} +7 z^4+a^7 z^3-2 a^5 z^3-a^3 z^3+5 a z^3-16 z^3 a^{-3} -13 z^3 a^{-5} -a^6 z^2+5 a^4 z^2+4 a^2 z^2+10 z^2 a^{-2} +9 z^2 a^{-4} -z^2-a^7 z+a^5 z+2 a^3 z-a z+4 z a^{-3} +3 z a^{-5} -2 a^4-3 a^2- a^{-2} - a^{-4} }[/math] |
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