K12a118
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+11 q^2-16 q+20-21 q^{-1} +20 q^{-2} -16 q^{-3} +12 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-32 t+43-32 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4+2 z^2+1 }[/math] |
| Determinant | 137 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+3 z^2 a^4+a^4-z^6 a^2-z^4 a^2+z^2 a^2+2 a^2-z^6-2 z^4-4 z^2-3+2 z^4 a^{-2} +4 z^2 a^{-2} +3 a^{-2} -z^2 a^{-4} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+4 a^5 z^9+6 a^3 z^9+6 a z^9+4 z^9 a^{-1} +3 a^6 z^8-3 a^4 z^8-11 a^2 z^8+4 z^8 a^{-2} -z^8+a^7 z^7-11 a^5 z^7-22 a^3 z^7-15 a z^7-z^7 a^{-1} +4 z^7 a^{-3} -11 a^6 z^6-12 a^4 z^6+3 a^2 z^6+z^6 a^{-2} +3 z^6 a^{-4} +2 z^6-4 a^7 z^5+4 a^5 z^5+17 a^3 z^5+10 a z^5-4 z^5 a^{-1} -4 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+15 a^4 z^4-a^2 z^4-12 z^4 a^{-2} -6 z^4 a^{-4} -10 z^4+5 a^7 z^3+4 a^5 z^3-4 a^3 z^3+4 z^3 a^{-1} -z^3 a^{-3} -2 z^3 a^{-5} -5 a^6 z^2-6 a^4 z^2+4 a^2 z^2+11 z^2 a^{-2} +4 z^2 a^{-4} +12 z^2-2 a^7 z-2 a^5 z-a z-z a^{-1} +z a^{-3} +z a^{-5} +a^6+a^4-2 a^2-3 a^{-2} - a^{-4} -3 }[/math] |
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