K12a992
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+11 q^4-21 q^3+31 q^2-39 q+43-40 q^{-1} +33 q^{-2} -23 q^{-3} +13 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+30 t^2-57 t+71-57 t^{-1} +30 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-4 z^4-2 z^2+1 }[/math] |
| Determinant | 265 |
| 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^4-5 z^4 a^{-2} +z^4 a^{-4} +3 z^4+a^4 z^2-a^2 z^2-4 z^2 a^{-2} +2 z^2 a^{-4} +a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a z^{11}+4 z^{11} a^{-1} +12 a^2 z^{10}+11 z^{10} a^{-2} +23 z^{10}+16 a^3 z^9+23 a z^9+20 z^9 a^{-1} +13 z^9 a^{-3} +12 a^4 z^8-8 a^2 z^8-12 z^8 a^{-2} +9 z^8 a^{-4} -41 z^8+5 a^5 z^7-29 a^3 z^7-67 a z^7-63 z^7 a^{-1} -26 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-22 a^4 z^6-18 a^2 z^6-3 z^6 a^{-2} -17 z^6 a^{-4} +z^6 a^{-6} +20 z^6-7 a^5 z^5+16 a^3 z^5+60 a z^5+69 z^5 a^{-1} +25 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+12 a^4 z^4+15 a^2 z^4+11 z^4 a^{-2} +12 z^4 a^{-4} -2 z^4 a^{-6} -z^4+2 a^5 z^3-6 a^3 z^3-26 a z^3-37 z^3 a^{-1} -16 z^3 a^{-3} +3 z^3 a^{-5} -3 a^4 z^2-a^2 z^2-7 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-6} +z^2+2 a^3 z+6 a z+8 z a^{-1} +4 z a^{-3} -a^2+ a^{-2} + a^{-4} }[/math] |
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