K12a678
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+16 q^5-23 q^4+27 q^3-28 q^2+26 q-20+14 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-19 t^2+41 t-51+41 t^{-1} -19 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+5 z^4+z^2+1 }[/math] |
| Determinant | 179 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+4 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} +2 z^4-2 a^2 z^2+z^2 a^{-2} -z^2 a^{-6} +3 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10}+4 a z^9+4 z^9 a^{-1} +11 z^9 a^{-3} +11 z^9 a^{-5} +3 a^2 z^8-27 z^8 a^{-2} -7 z^8 a^{-4} +11 z^8 a^{-6} -6 z^8+a^3 z^7-9 a z^7-17 z^7 a^{-1} -34 z^7 a^{-3} -19 z^7 a^{-5} +8 z^7 a^{-7} -11 a^2 z^6+29 z^6 a^{-2} +2 z^6 a^{-4} -17 z^6 a^{-6} +4 z^6 a^{-8} -5 z^6-4 a^3 z^5-a z^5+10 z^5 a^{-1} +35 z^5 a^{-3} +16 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4-21 z^4 a^{-2} -3 z^4 a^{-4} +9 z^4 a^{-6} -5 z^4 a^{-8} +9 z^4+5 a^3 z^3+10 a z^3-16 z^3 a^{-3} -6 z^3 a^{-5} +4 z^3 a^{-7} -z^3 a^{-9} -6 a^2 z^2+4 z^2 a^{-2} +3 z^2 a^{-4} +z^2 a^{-8} -6 z^2-2 a^3 z-4 a z-2 z a^{-1} +z a^{-3} +z a^{-5} +a^2+ a^{-2} +3 }[/math] |
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