K12n666
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+3 q^{10}-6 q^9+10 q^8-13 q^7+13 q^6-13 q^5+11 q^4-6 q^3+4 q^2-q }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+10 t^2-16 t+19-16 t^{-1} +10 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+6 z^4+4 z^2+1 }[/math] |
| Determinant | 81 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-6} -z^6 a^{-4} +6 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-4} +13 z^4 a^{-6} -4 z^4 a^{-8} -z^2 a^{-4} +10 z^2 a^{-6} -5 z^2 a^{-8} +2 a^{-4} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +z^9 a^{-5} +4 z^9 a^{-7} +3 z^9 a^{-9} -2 z^8 a^{-6} +2 z^8 a^{-8} +4 z^8 a^{-10} -z^7 a^{-5} -9 z^7 a^{-7} -4 z^7 a^{-9} +4 z^7 a^{-11} +4 z^6 a^{-4} +9 z^6 a^{-6} -2 z^6 a^{-8} -4 z^6 a^{-10} +3 z^6 a^{-12} +z^5 a^{-3} +2 z^5 a^{-5} +14 z^5 a^{-7} +7 z^5 a^{-9} -5 z^5 a^{-11} +z^5 a^{-13} -9 z^4 a^{-4} -15 z^4 a^{-6} -z^4 a^{-8} -z^4 a^{-10} -6 z^4 a^{-12} -2 z^3 a^{-3} -2 z^3 a^{-5} -8 z^3 a^{-7} -7 z^3 a^{-9} -z^3 a^{-11} -2 z^3 a^{-13} +3 z^2 a^{-4} +9 z^2 a^{-6} +4 z^2 a^{-8} +z^2 a^{-10} +3 z^2 a^{-12} -2 z a^{-5} -z a^{-7} +z a^{-9} +z a^{-11} +z a^{-13} +2 a^{-4} - a^{-8} }[/math] |
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