K12a847
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+9 q^8-17 q^7+24 q^6-28 q^5+30 q^4-27 q^3+22 q^2-15 q+8-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+24 t^2-39 t+45-39 t^{-1} +24 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-4 z^4+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +4 z^6 a^{-4} -2 z^6 a^{-6} -7 z^4 a^{-2} +7 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +z^4-8 z^2 a^{-2} +9 z^2 a^{-4} -5 z^2 a^{-6} +2 z^2 a^{-8} +3 z^2-4 a^{-2} +5 a^{-4} -2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +13 z^{10} a^{-4} +9 z^{10} a^{-6} +3 z^9 a^{-1} +7 z^9 a^{-3} +22 z^9 a^{-5} +18 z^9 a^{-7} -11 z^8 a^{-2} -30 z^8 a^{-4} +3 z^8 a^{-6} +21 z^8 a^{-8} +z^8-13 z^7 a^{-1} -47 z^7 a^{-3} -82 z^7 a^{-5} -32 z^7 a^{-7} +16 z^7 a^{-9} -z^6 a^{-2} -10 z^6 a^{-4} -64 z^6 a^{-6} -41 z^6 a^{-8} +9 z^6 a^{-10} -5 z^6+20 z^5 a^{-1} +65 z^5 a^{-3} +74 z^5 a^{-5} +4 z^5 a^{-7} -21 z^5 a^{-9} +4 z^5 a^{-11} +24 z^4 a^{-2} +51 z^4 a^{-4} +70 z^4 a^{-6} +28 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +9 z^4-13 z^3 a^{-1} -32 z^3 a^{-3} -21 z^3 a^{-5} +8 z^3 a^{-7} +9 z^3 a^{-9} -z^3 a^{-11} -20 z^2 a^{-2} -30 z^2 a^{-4} -25 z^2 a^{-6} -8 z^2 a^{-8} -7 z^2+3 z a^{-1} +6 z a^{-3} +2 z a^{-5} -z a^{-7} +4 a^{-2} +5 a^{-4} +2 a^{-6} +2 }[/math] |
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