K12a793
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-24 q^3+35 q^2-43 q+46-42 q^{-1} +35 q^{-2} -23 q^{-3} +12 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+32 t^2-62 t+77-62 t^{-1} +32 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-2 z^4+z^2+1 }[/math] |
| Determinant | 285 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-4 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +4 z^4+a^4 z^2-a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} +2 z^2-a^4+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a z^{11}+4 z^{11} a^{-1} +11 a^2 z^{10}+13 z^{10} a^{-2} +24 z^{10}+14 a^3 z^9+25 a z^9+28 z^9 a^{-1} +17 z^9 a^{-3} +11 a^4 z^8+a^2 z^8-8 z^8 a^{-2} +12 z^8 a^{-4} -30 z^8+5 a^5 z^7-17 a^3 z^7-57 a z^7-71 z^7 a^{-1} -31 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-19 a^4 z^6-32 a^2 z^6-18 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -8 z^6-8 a^5 z^5-3 a^3 z^5+26 a z^5+48 z^5 a^{-1} +20 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+12 a^4 z^4+25 a^2 z^4+16 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +15 z^4+4 a^5 z^3+10 a^3 z^3+4 a z^3-9 z^3 a^{-1} -5 z^3 a^{-3} +2 z^3 a^{-5} -2 a^4 z^2-4 a^2 z^2-3 z^2 a^{-2} -2 z^2 a^{-4} -3 z^2-2 a^3 z-3 a z-z a^{-1} -a^4-2 a^2 }[/math] |
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