K12a560
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+16 q^2-22 q+26-27 q^{-1} +25 q^{-2} -19 q^{-3} +13 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-41 t+57-41 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 173 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+3 z^2 a^4+2 a^4-z^6 a^2-z^4 a^2-2 z^2 a^2-a^2-z^6+z^2+1+2 z^4 a^{-2} +z^2 a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+8 a^2 z^{10}+5 z^{10}+4 a^5 z^9+10 a^3 z^9+16 a z^9+10 z^9 a^{-1} +3 a^6 z^8-9 a^2 z^8+11 z^8 a^{-2} +5 z^8+a^7 z^7-10 a^5 z^7-32 a^3 z^7-44 a z^7-15 z^7 a^{-1} +8 z^7 a^{-3} -11 a^6 z^6-19 a^4 z^6-12 a^2 z^6-18 z^6 a^{-2} +4 z^6 a^{-4} -26 z^6-4 a^7 z^5+3 a^5 z^5+29 a^3 z^5+45 a z^5+11 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +13 a^6 z^4+23 a^4 z^4+19 a^2 z^4+12 z^4 a^{-2} -5 z^4 a^{-4} +26 z^4+5 a^7 z^3+5 a^5 z^3-12 a^3 z^3-22 a z^3-5 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -6 a^6 z^2-10 a^4 z^2-9 a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} -9 z^2-2 a^7 z-2 a^5 z+2 a^3 z+3 a z+z a^{-1} +a^6+2 a^4+a^2+1 }[/math] |
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