K12a445
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+13 q-19+25 q^{-1} -26 q^{-2} +26 q^{-3} -22 q^{-4} +15 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-20 t^2+36 t-43+36 t^{-1} -20 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 171 |
| 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+7 a^4 z^4-11 a^2 z^4-z^4 a^{-2} +8 z^4-2 a^6 z^2+8 a^4 z^2-11 a^2 z^2-3 z^2 a^{-2} +11 z^2-a^6+2 a^4-3 a^2-2 a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+7 a^2 z^{10}+3 z^{10}+8 a^5 z^9+13 a^3 z^9+9 a z^9+4 z^9 a^{-1} +10 a^6 z^8+10 a^4 z^8-3 a^2 z^8+3 z^8 a^{-2} +8 a^7 z^7-3 a^5 z^7-26 a^3 z^7-26 a z^7-10 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-14 a^6 z^6-34 a^4 z^6-25 a^2 z^6-11 z^6 a^{-2} -20 z^6+a^9 z^5-12 a^7 z^5-14 a^5 z^5+10 a^3 z^5+18 a z^5+3 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+8 a^6 z^4+32 a^4 z^4+35 a^2 z^4+13 z^4 a^{-2} +29 z^4-a^9 z^3+7 a^7 z^3+15 a^5 z^3+2 a^3 z^3-4 a z^3+6 z^3 a^{-1} +5 z^3 a^{-3} +a^8 z^2-3 a^6 z^2-13 a^4 z^2-21 a^2 z^2-6 z^2 a^{-2} -18 z^2-2 a^7 z-2 a^5 z-a z-3 z a^{-1} -2 z a^{-3} +a^6+2 a^4+3 a^2+2 a^{-2} +5 }[/math] |
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