K12a486
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-23 q^3+33 q^2-41 q+44-40 q^{-1} +33 q^{-2} -22 q^{-3} +12 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+31 t^2-59 t+73-59 t^{-1} +31 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-3 z^4+1 }[/math] |
| Determinant | 273 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-4 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +3 z^4+a^4 z^2-z^2 a^{-2} +z^2 a^{-4} -z^2-a^4+3 a^2+ a^{-2} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +9 a^2 z^{10}+11 z^{10} a^{-2} +20 z^{10}+13 a^3 z^9+26 a z^9+29 z^9 a^{-1} +16 z^9 a^{-3} +11 a^4 z^8+8 a^2 z^8-z^8 a^{-2} +12 z^8 a^{-4} -16 z^8+5 a^5 z^7-15 a^3 z^7-55 a z^7-69 z^7 a^{-1} -29 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-20 a^4 z^6-42 a^2 z^6-29 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -27 z^6-8 a^5 z^5-4 a^3 z^5+24 a z^5+45 z^5 a^{-1} +18 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+13 a^4 z^4+29 a^2 z^4+23 z^4 a^{-2} +13 z^4 a^{-4} -z^4 a^{-6} +24 z^4+4 a^5 z^3+8 a^3 z^3+2 a z^3-9 z^3 a^{-1} -5 z^3 a^{-3} +2 z^3 a^{-5} -2 a^4 z^2-2 a^2 z^2-3 z^2 a^{-2} -3 z^2 a^{-4} -a^3 z-a z+z a^{-1} +z a^{-3} -a^4-3 a^2- a^{-2} -2 }[/math] |
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