K12a525
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+8 q^2-13 q+18-20 q^{-1} +22 q^{-2} -19 q^{-3} +15 q^{-4} -11 q^{-5} +6 q^{-6} -3 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-33 t+45-33 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4+z^2+1 }[/math] |
| Determinant | 141 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-3 z^2 a^6-3 a^6+3 z^4 a^4+5 z^2 a^4+2 a^4-z^6 a^2-z^4 a^2+a^2-z^6-2 z^4-2 z^2+z^4 a^{-2} +z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+3 a^6 z^{10}+7 a^4 z^{10}+4 a^2 z^{10}+3 a^7 z^9+7 a^5 z^9+12 a^3 z^9+8 a z^9+a^8 z^8-9 a^6 z^8-15 a^4 z^8+6 a^2 z^8+11 z^8-15 a^7 z^7-44 a^5 z^7-46 a^3 z^7-6 a z^7+11 z^7 a^{-1} -5 a^8 z^6-3 a^6 z^6-16 a^4 z^6-40 a^2 z^6+8 z^6 a^{-2} -14 z^6+25 a^7 z^5+69 a^5 z^5+48 a^3 z^5-13 a z^5-13 z^5 a^{-1} +4 z^5 a^{-3} +8 a^8 z^4+25 a^6 z^4+47 a^4 z^4+40 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +2 z^4-17 a^7 z^3-42 a^5 z^3-25 a^3 z^3+6 a z^3+4 z^3 a^{-1} -2 z^3 a^{-3} -5 a^8 z^2-18 a^6 z^2-25 a^4 z^2-14 a^2 z^2+2 z^2 a^{-2} +4 a^7 z+11 a^5 z+9 a^3 z+2 a z+a^8+3 a^6+2 a^4-a^2 }[/math] |
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