K12a318
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-11 q^2+18 q-25+30 q^{-1} -31 q^{-2} +29 q^{-3} -22 q^{-4} +15 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-22 t^2+43 t-53+43 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^2+1 }[/math] |
| Determinant | 199 |
| 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^4-12 a^2 z^4-z^4 a^{-2} +6 z^4-3 a^6 z^2+13 a^4 z^2-13 a^2 z^2-z^2 a^{-2} +6 z^2-3 a^6+7 a^4-5 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+13 a^2 z^{10}+7 z^{10}+9 a^5 z^9+16 a^3 z^9+16 a z^9+9 z^9 a^{-1} +9 a^6 z^8+4 a^4 z^8-19 a^2 z^8+5 z^8 a^{-2} -9 z^8+6 a^7 z^7-10 a^5 z^7-46 a^3 z^7-57 a z^7-26 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-15 a^6 z^6-33 a^4 z^6-19 a^2 z^6-14 z^6 a^{-2} -18 z^6+a^9 z^5-8 a^7 z^5+35 a^3 z^5+47 a z^5+19 z^5 a^{-1} -2 z^5 a^{-3} -4 a^8 z^4+17 a^6 z^4+46 a^4 z^4+40 a^2 z^4+10 z^4 a^{-2} +25 z^4-2 a^9 z^3+5 a^7 z^3+10 a^5 z^3-4 a^3 z^3-10 a z^3-2 z^3 a^{-1} +z^3 a^{-3} +a^8 z^2-11 a^6 z^2-27 a^4 z^2-23 a^2 z^2-z^2 a^{-2} -9 z^2+a^9 z-2 a^7 z-5 a^5 z-3 a^3 z-2 a z-z a^{-1} +3 a^6+7 a^4+5 a^2+2 }[/math] |
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