K12n250
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+2 q^4-3 q^3+5 q^2-6 q+7-6 q^{-1} +5 q^{-2} -3 q^{-3} +2 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^2-10 t+15-10 t^{-1} +3 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^4+2 z^2+1 }[/math] |
| Determinant | 41 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^4-a^4+z^4 a^2+2 z^2 a^2+2 a^2+z^4-1+z^4 a^{-2} +2 z^2 a^{-2} +2 a^{-2} -z^2 a^{-4} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+a^3 z^9+3 a z^9+2 z^9 a^{-1} -6 a^2 z^8+2 z^8 a^{-2} -4 z^8-6 a^3 z^7-17 a z^7-9 z^7 a^{-1} +2 z^7 a^{-3} +2 a^4 z^6+15 a^2 z^6-6 z^6 a^{-2} +2 z^6 a^{-4} +5 z^6+a^5 z^5+16 a^3 z^5+36 a z^5+15 z^5 a^{-1} -5 z^5 a^{-3} +z^5 a^{-5} -7 a^4 z^4-16 a^2 z^4+4 z^4 a^{-2} -6 z^4 a^{-4} +z^4-4 a^5 z^3-20 a^3 z^3-27 a z^3-7 z^3 a^{-1} +z^3 a^{-3} -3 z^3 a^{-5} +5 a^4 z^2+7 a^2 z^2+3 z^2 a^{-2} +3 z^2 a^{-4} +2 z^2+3 a^5 z+7 a^3 z+6 a z+2 z a^{-1} +z a^{-3} +z a^{-5} -a^4-2 a^2-2 a^{-2} - a^{-4} -1 }[/math] |
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