K12a137
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-11 q^2+19 q-26+32 q^{-1} -34 q^{-2} +31 q^{-3} -25 q^{-4} +17 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-26 t^2+46 t-53+46 t^{-1} -26 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+2 z^4-2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-7 a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+5 a^4 z^2-6 a^2 z^2-z^2 a^{-2} +2 z^2+a^4-a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+7 a^4 z^{10}+14 a^2 z^{10}+7 z^{10}+11 a^5 z^9+21 a^3 z^9+19 a z^9+9 z^9 a^{-1} +11 a^6 z^8+6 a^4 z^8-16 a^2 z^8+5 z^8 a^{-2} -6 z^8+8 a^7 z^7-10 a^5 z^7-57 a^3 z^7-65 a z^7-25 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-13 a^6 z^6-35 a^4 z^6-31 a^2 z^6-14 z^6 a^{-2} -27 z^6+a^9 z^5-10 a^7 z^5-3 a^5 z^5+43 a^3 z^5+55 a z^5+18 z^5 a^{-1} -2 z^5 a^{-3} -5 a^8 z^4+5 a^6 z^4+34 a^4 z^4+47 a^2 z^4+11 z^4 a^{-2} +34 z^4-a^9 z^3+5 a^7 z^3+7 a^5 z^3-9 a^3 z^3-14 a z^3-3 z^3 a^{-1} +z^3 a^{-3} +2 a^8 z^2-12 a^4 z^2-17 a^2 z^2-2 z^2 a^{-2} -9 z^2-a^7 z-3 a^5 z-a^3 z+a z+a^4+a^2- a^{-2} }[/math] |
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