K12n490
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+10 q^2-12 q+13-12 q^{-1} +10 q^{-2} -6 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^2-19 t+29-19 t^{-1} +5 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^4+z^2+1 }[/math] |
| Determinant | 77 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^4+z^4 a^2-z^2 a^2-a^2+3 z^4+5 z^2+3+z^4 a^{-2} -z^2 a^{-2} - a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+a^3 z^9+5 a z^9+4 z^9 a^{-1} -2 a^2 z^8+6 z^8 a^{-2} +4 z^8-3 a^3 z^7-18 a z^7-10 z^7 a^{-1} +5 z^7 a^{-3} +3 a^4 z^6+4 a^2 z^6-17 z^6 a^{-2} +3 z^6 a^{-4} -19 z^6+a^5 z^5+10 a^3 z^5+33 a z^5+12 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} -7 a^4 z^4+20 z^4 a^{-2} -6 z^4 a^{-4} +33 z^4-3 a^5 z^3-15 a^3 z^3-23 a z^3-3 z^3 a^{-1} +6 z^3 a^{-3} -2 z^3 a^{-5} +3 a^4 z^2-5 a^2 z^2-9 z^2 a^{-2} +z^2 a^{-4} -18 z^2+2 a^5 z+5 a^3 z+4 a z-z a^{-3} +a^2+ a^{-2} +3 }[/math] |
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