K12n78
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+2 q^4-4 q^3+7 q^2-9 q+11-10 q^{-1} +9 q^{-2} -6 q^{-3} +4 q^{-4} -2 q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^2-16 t+23-16 t^{-1} +5 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^4+4 z^2+1 }[/math] |
| Determinant | 65 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^2 a^4-2 a^4+2 z^4 a^2+4 z^2 a^2+3 a^2+2 z^4+2 z^2+z^4 a^{-2} +z^2 a^{-2} + a^{-2} -z^2 a^{-4} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+2 a^3 z^9+4 a z^9+2 z^9 a^{-1} +a^4 z^8-2 a^2 z^8+2 z^8 a^{-2} -z^8-8 a^3 z^7-15 a z^7-5 z^7 a^{-1} +2 z^7 a^{-3} +4 a^2 z^6-2 z^6 a^{-2} +2 z^6 a^{-4} +3 a^5 z^5+18 a^3 z^5+27 a z^5+9 z^5 a^{-1} -2 z^5 a^{-3} +z^5 a^{-5} -7 a^4 z^4-7 a^2 z^4-z^4 a^{-2} -5 z^4 a^{-4} +4 z^4-9 a^5 z^3-23 a^3 z^3-19 a z^3-5 z^3 a^{-1} -3 z^3 a^{-3} -3 z^3 a^{-5} +6 a^4 z^2+7 a^2 z^2+2 z^2 a^{-2} +3 z^2 a^{-4} +5 a^5 z+9 a^3 z+5 a z+z a^{-1} +2 z a^{-3} +2 z a^{-5} -2 a^4-3 a^2- a^{-2} - a^{-4} }[/math] |
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