K12a905
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+8 q^6-15 q^5+22 q^4-26 q^3+30 q^2-28 q+23-17 q^{-1} +10 q^{-2} -4 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+20 t^2-43 t+55-43 t^{-1} +20 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-4 z^4+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-4 z^4 a^{-2} -z^4 a^{-4} +z^4 a^{-6} -z^4+a^2 z^2-z^2 a^{-2} +z^2 a^{-4} +z^2 a^{-6} -z^2+a^2+2 a^{-2} + a^{-4} - a^{-6} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +10 z^{10} a^{-2} +16 z^{10} a^{-4} +6 z^{10} a^{-6} +17 z^9 a^{-1} +14 z^9 a^{-3} +z^9 a^{-5} +4 z^9 a^{-7} -9 z^8 a^{-2} -55 z^8 a^{-4} -25 z^8 a^{-6} +z^8 a^{-8} +20 z^8+17 a z^7-28 z^7 a^{-1} -65 z^7 a^{-3} -38 z^7 a^{-5} -18 z^7 a^{-7} +10 a^2 z^6-22 z^6 a^{-2} +59 z^6 a^{-4} +34 z^6 a^{-6} -4 z^6 a^{-8} -33 z^6+4 a^3 z^5-23 a z^5+2 z^5 a^{-1} +67 z^5 a^{-3} +64 z^5 a^{-5} +26 z^5 a^{-7} +a^4 z^4-7 a^2 z^4+12 z^4 a^{-2} -29 z^4 a^{-4} -18 z^4 a^{-6} +4 z^4 a^{-8} +11 z^4+11 a z^3+5 z^3 a^{-1} -27 z^3 a^{-3} -33 z^3 a^{-5} -12 z^3 a^{-7} +3 a^2 z^2+6 z^2 a^{-2} +9 z^2 a^{-4} +4 z^2 a^{-6} +4 z^2-2 a z-2 z a^{-1} +3 z a^{-3} +3 z a^{-5} -a^2-2 a^{-2} + a^{-4} + a^{-6} -2 }[/math] |
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