K12n686
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^9+5 q^8-9 q^7+13 q^6-15 q^5+16 q^4-14 q^3+11 q^2-7 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+13 t^2-19 t+21-19 t^{-1} +13 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+3 z^4+4 z^2+1 }[/math] |
| Determinant | 97 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -3 z^4 a^{-2} +8 z^4 a^{-4} -2 z^4 a^{-6} -z^2 a^{-2} +4 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} + a^{-2} - a^{-4} +3 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-3} +9 z^9 a^{-5} +4 z^9 a^{-7} +4 z^8 a^{-2} +2 z^8 a^{-4} +2 z^8 a^{-6} +4 z^8 a^{-8} +z^7 a^{-1} -17 z^7 a^{-3} -25 z^7 a^{-5} -4 z^7 a^{-7} +3 z^7 a^{-9} -15 z^6 a^{-2} -22 z^6 a^{-4} -9 z^6 a^{-6} -z^6 a^{-8} +z^6 a^{-10} -3 z^5 a^{-1} +14 z^5 a^{-3} +17 z^5 a^{-5} +15 z^4 a^{-2} +20 z^4 a^{-4} -5 z^4 a^{-6} -6 z^4 a^{-8} +4 z^4 a^{-10} +2 z^3 a^{-1} -z^3 a^{-3} -5 z^3 a^{-5} -4 z^3 a^{-7} +z^3 a^{-9} +3 z^3 a^{-11} -2 z^2 a^{-2} -2 z^2 a^{-4} +9 z^2 a^{-6} +7 z^2 a^{-8} -2 z^2 a^{-10} +2 z a^{-7} -2 z a^{-11} - a^{-2} - a^{-4} -3 a^{-6} -2 a^{-8} }[/math] |
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