K12a383
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-8 q^2+14 q-20+24 q^{-1} -25 q^{-2} +24 q^{-3} -19 q^{-4} +13 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-20 t^2+34 t-39+34 t^{-1} -20 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 163 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+8 a^4 z^4-11 a^2 z^4-z^4 a^{-2} +7 z^4-3 a^6 z^2+11 a^4 z^2-12 a^2 z^2-2 z^2 a^{-2} +7 z^2-2 a^6+5 a^4-4 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+8 a^2 z^{10}+4 z^{10}+7 a^5 z^9+14 a^3 z^9+13 a z^9+6 z^9 a^{-1} +7 a^6 z^8+5 a^4 z^8-8 a^2 z^8+4 z^8 a^{-2} -2 z^8+5 a^7 z^7-10 a^5 z^7-42 a^3 z^7-47 a z^7-19 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-11 a^6 z^6-31 a^4 z^6-27 a^2 z^6-14 z^6 a^{-2} -24 z^6+a^9 z^5-6 a^7 z^5+7 a^5 z^5+41 a^3 z^5+47 a z^5+17 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+11 a^6 z^4+45 a^4 z^4+47 a^2 z^4+14 z^4 a^{-2} +32 z^4-2 a^9 z^3+a^7 z^3-13 a^3 z^3-18 a z^3-6 z^3 a^{-1} +2 z^3 a^{-3} +2 a^8 z^2-8 a^6 z^2-25 a^4 z^2-25 a^2 z^2-4 z^2 a^{-2} -14 z^2+a^9 z-a^5 z+a^3 z+a z+2 a^6+5 a^4+4 a^2+2 }[/math] |
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