K12n178
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+12 q^2-15 q+17-16 q^{-1} +14 q^{-2} -9 q^{-3} +5 q^{-4} -2 q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+9 t^2-24 t+33-24 t^{-1} +9 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+3 z^4+3 z^2+1 }[/math] |
| Determinant | 101 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6+3 a^2 z^4+2 z^4 a^{-2} -2 z^4-2 a^4 z^2+6 a^2 z^2+3 z^2 a^{-2} -z^2 a^{-4} -3 z^2-2 a^4+4 a^2+2 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+2 a^3 z^9+5 a z^9+3 z^9 a^{-1} +a^4 z^8+2 a^2 z^8+5 z^8 a^{-2} +6 z^8-3 a^3 z^7-4 a z^7+4 z^7 a^{-1} +5 z^7 a^{-3} +2 a^4 z^6+3 a^2 z^6-3 z^6 a^{-2} +3 z^6 a^{-4} -5 z^6+3 a^5 z^5+9 a^3 z^5+2 a z^5-12 z^5 a^{-1} -7 z^5 a^{-3} +z^5 a^{-5} -8 a^4 z^4-16 a^2 z^4-5 z^4 a^{-2} -5 z^4 a^{-4} -8 z^4-7 a^5 z^3-16 a^3 z^3-7 a z^3+7 z^3 a^{-1} +3 z^3 a^{-3} -2 z^3 a^{-5} +7 a^4 z^2+13 a^2 z^2+6 z^2 a^{-2} +3 z^2 a^{-4} +9 z^2+4 a^5 z+7 a^3 z+3 a z-z a^{-1} +z a^{-5} -2 a^4-4 a^2-2 a^{-2} - a^{-4} -2 }[/math] |
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