K12n491
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+3 q^2-6 q+9-10 q^{-1} +12 q^{-2} -10 q^{-3} +8 q^{-4} -6 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+7 t^2-16 t+21-16 t^{-1} +7 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+z^4+3 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+4 z^2 a^4+a^4-z^6 a^2-3 z^4 a^2-3 z^2 a^2+2 z^4+4 z^2+2-z^2 a^{-2} - a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^{10}+2 a^2 z^{10}+4 a^5 z^9+8 a^3 z^9+4 a z^9+3 a^6 z^8-3 a^4 z^8-3 a^2 z^8+3 z^8+a^7 z^7-16 a^5 z^7-34 a^3 z^7-16 a z^7+z^7 a^{-1} -12 a^6 z^6-11 a^4 z^6-9 a^2 z^6-10 z^6-4 a^7 z^5+17 a^5 z^5+47 a^3 z^5+26 a z^5+12 a^6 z^4+18 a^4 z^4+20 a^2 z^4+3 z^4 a^{-2} +17 z^4+4 a^7 z^3-8 a^5 z^3-30 a^3 z^3-18 a z^3+z^3 a^{-1} +z^3 a^{-3} -4 a^6 z^2-9 a^4 z^2-12 a^2 z^2-3 z^2 a^{-2} -10 z^2-a^7 z+3 a^5 z+8 a^3 z+5 a z-z a^{-3} +a^6+a^4+ a^{-2} +2 }[/math] |
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