K12a359
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-6 q^5+15 q^4-26 q^3+38 q^2-46 q+49-45 q^{-1} +36 q^{-2} -24 q^{-3} +13 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+33 t^2-67 t+85-67 t^{-1} +33 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-z^4+1 }[/math] |
| Determinant | 305 |
| 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^4-3 z^4 a^{-2} +z^4 a^{-4} +4 z^4+a^4 z^2-2 a^2 z^2+z^2 a^{-2} +a^2+3 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a z^{11}+4 z^{11} a^{-1} +13 a^2 z^{10}+14 z^{10} a^{-2} +27 z^{10}+17 a^3 z^9+35 a z^9+38 z^9 a^{-1} +20 z^9 a^{-3} +12 a^4 z^8-3 a^2 z^8+z^8 a^{-2} +15 z^8 a^{-4} -29 z^8+5 a^5 z^7-30 a^3 z^7-95 a z^7-98 z^7 a^{-1} -32 z^7 a^{-3} +6 z^7 a^{-5} +a^6 z^6-21 a^4 z^6-34 a^2 z^6-44 z^6 a^{-2} -24 z^6 a^{-4} +z^6 a^{-6} -31 z^6-7 a^5 z^5+20 a^3 z^5+79 a z^5+71 z^5 a^{-1} +13 z^5 a^{-3} -6 z^5 a^{-5} -a^6 z^4+13 a^4 z^4+36 a^2 z^4+29 z^4 a^{-2} +9 z^4 a^{-4} +42 z^4+2 a^5 z^3-7 a^3 z^3-23 a z^3-19 z^3 a^{-1} -5 z^3 a^{-3} -4 a^4 z^2-9 a^2 z^2+z^2 a^{-4} -6 z^2+a^3 z+2 a z+2 z a^{-1} +2 z a^{-3} +z a^{-5} -a^2-3 a^{-2} - a^{-4} -2 }[/math] |
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