K12a99
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-17 q^3+25 q^2-31 q+35-32 q^{-1} +27 q^{-2} -19 q^{-3} +11 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+24 t^2-47 t+59-47 t^{-1} +24 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 217 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-6 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +13 z^4+a^4 z^2-7 a^2 z^2-10 z^2 a^{-2} +2 z^2 a^{-4} +16 z^2-3 a^2-5 a^{-2} + a^{-4} +8 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +5 a^2 z^{10}+4 z^{10} a^{-2} +9 z^{10}+10 a^3 z^9+22 a z^9+19 z^9 a^{-1} +7 z^9 a^{-3} +10 a^4 z^8+16 a^2 z^8+14 z^8 a^{-2} +7 z^8 a^{-4} +13 z^8+5 a^5 z^7-10 a^3 z^7-39 a z^7-31 z^7 a^{-1} -3 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-20 a^4 z^6-57 a^2 z^6-46 z^6 a^{-2} -13 z^6 a^{-4} +z^6 a^{-6} -68 z^6-9 a^5 z^5-12 a^3 z^5+3 a z^5-2 z^5 a^{-1} -17 z^5 a^{-3} -9 z^5 a^{-5} -a^6 z^4+12 a^4 z^4+51 a^2 z^4+45 z^4 a^{-2} +8 z^4 a^{-4} -2 z^4 a^{-6} +73 z^4+4 a^5 z^3+15 a^3 z^3+23 a z^3+26 z^3 a^{-1} +21 z^3 a^{-3} +7 z^3 a^{-5} -3 a^4 z^2-19 a^2 z^2-21 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} -33 z^2-4 a^3 z-10 a z-12 z a^{-1} -8 z a^{-3} -2 z a^{-5} +3 a^2+5 a^{-2} + a^{-4} +8 }[/math] |
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