K12a1127
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+5 q^4-8 q^3+11 q^2-14 q+15-14 q^{-1} +11 q^{-2} -8 q^{-3} +5 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-24 t+41-24 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4-8 z^2+1 }[/math] |
| Determinant | 97 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-2 z^2 a^4+z^4 a^2-2 z^2 a^2-a^2+2 z^4+1+z^4 a^{-2} -2 z^2 a^{-2} - a^{-2} -2 z^2 a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+2 z^{10} a^{-2} +4 z^{10}+3 a^3 z^9-a z^9-z^9 a^{-1} +3 z^9 a^{-3} +3 a^4 z^8-4 a^2 z^8-4 z^8 a^{-2} +3 z^8 a^{-4} -14 z^8+2 a^5 z^7-9 a^3 z^7-9 z^7 a^{-3} +2 z^7 a^{-5} +a^6 z^6-9 a^4 z^6+a^2 z^6+z^6 a^{-2} -9 z^6 a^{-4} +z^6 a^{-6} +22 z^6-6 a^5 z^5+11 a^3 z^5+a z^5+z^5 a^{-1} +11 z^5 a^{-3} -6 z^5 a^{-5} -4 a^6 z^4+7 a^4 z^4+6 a^2 z^4+6 z^4 a^{-2} +7 z^4 a^{-4} -4 z^4 a^{-6} -10 z^4+3 a^5 z^3-9 a^3 z^3+4 a z^3+4 z^3 a^{-1} -9 z^3 a^{-3} +3 z^3 a^{-5} +4 a^6 z^2-3 a^4 z^2-6 a^2 z^2-6 z^2 a^{-2} -3 z^2 a^{-4} +4 z^2 a^{-6} +2 z^2+2 a^3 z-2 a z-2 z a^{-1} +2 z a^{-3} -a^6+a^2+ a^{-2} - a^{-6} +1 }[/math] |
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