K12a209
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-22 q^3+33 q^2-40 q+44-41 q^{-1} +33 q^{-2} -23 q^{-3} +13 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+29 t^2-60 t+77-60 t^{-1} +29 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+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} +4 z^6+a^4 z^4-5 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +9 z^4+a^4 z^2-6 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +9 z^2+a^4-3 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +11 a^2 z^{10}+10 z^{10} a^{-2} +21 z^{10}+16 a^3 z^9+32 a z^9+30 z^9 a^{-1} +14 z^9 a^{-3} +12 a^4 z^8+a^2 z^8+4 z^8 a^{-2} +11 z^8 a^{-4} -18 z^8+5 a^5 z^7-29 a^3 z^7-88 a z^7-80 z^7 a^{-1} -21 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-22 a^4 z^6-42 a^2 z^6-46 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} -44 z^6-7 a^5 z^5+18 a^3 z^5+78 a z^5+66 z^5 a^{-1} +5 z^5 a^{-3} -8 z^5 a^{-5} -a^6 z^4+13 a^4 z^4+46 a^2 z^4+50 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +69 z^4+2 a^5 z^3-8 a^3 z^3-28 a z^3-19 z^3 a^{-1} +2 z^3 a^{-3} +3 z^3 a^{-5} -5 a^4 z^2-20 a^2 z^2-19 z^2 a^{-2} -4 z^2 a^{-4} -30 z^2+2 a^3 z+4 a z+2 z a^{-1} +a^4+3 a^2+ a^{-2} +4 }[/math] |
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