K12a169
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+2 q^2-3 q+5-5 q^{-1} +6 q^{-2} -6 q^{-3} +6 q^{-4} -5 q^{-5} +4 q^{-6} -3 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-12 t+17-12 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4+4 z^2+1 }[/math] |
| Determinant | 49 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^8-a^8+z^4 a^6+2 z^2 a^6+a^6+z^4 a^4+z^2 a^4+z^4 a^2+z^2 a^2+z^4+2 z^2+2-z^2 a^{-2} - a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^7 z^{11}+a^5 z^{11}+2 a^8 z^{10}+4 a^6 z^{10}+2 a^4 z^{10}+a^9 z^9-4 a^7 z^9-3 a^5 z^9+2 a^3 z^9-14 a^8 z^8-25 a^6 z^8-9 a^4 z^8+2 a^2 z^8-7 a^9 z^7-3 a^7 z^7-4 a^5 z^7-6 a^3 z^7+2 a z^7+32 a^8 z^6+50 a^6 z^6+12 a^4 z^6-4 a^2 z^6+2 z^6+16 a^9 z^5+24 a^7 z^5+14 a^5 z^5+2 a^3 z^5-2 a z^5+2 z^5 a^{-1} -28 a^8 z^4-39 a^6 z^4-9 a^4 z^4+2 z^4 a^{-2} -14 a^9 z^3-23 a^7 z^3-8 a^5 z^3+a^3 z^3-a z^3+z^3 a^{-3} +9 a^8 z^2+12 a^6 z^2+4 a^4 z^2-2 z^2 a^{-2} -3 z^2+4 a^9 z+5 a^7 z+a^5 z-z a^{-1} -z a^{-3} -a^8-a^6+ a^{-2} +2 }[/math] |
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