K12a696
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-13 q^3+24 q^2-34 q+42-44 q^{-1} +41 q^{-2} -33 q^{-3} +22 q^{-4} -12 q^{-5} +5 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+29 t^2-61 t+79-61 t^{-1} +29 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^4-z^2+1 }[/math] |
| Determinant | 277 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-8 a^2 z^4-2 z^4 a^{-2} +8 z^4-a^6 z^2+4 a^4 z^2-8 a^2 z^2-2 z^2 a^{-2} +6 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+9 a^4 z^{10}+22 a^2 z^{10}+13 z^{10}+10 a^5 z^9+27 a^3 z^9+40 a z^9+23 z^9 a^{-1} +5 a^6 z^8-7 a^4 z^8-22 a^2 z^8+22 z^8 a^{-2} +12 z^8+a^7 z^7-26 a^5 z^7-89 a^3 z^7-106 a z^7-31 z^7 a^{-1} +13 z^7 a^{-3} -13 a^6 z^6-29 a^4 z^6-50 a^2 z^6-32 z^6 a^{-2} +5 z^6 a^{-4} -71 z^6-2 a^7 z^5+22 a^5 z^5+80 a^3 z^5+80 a z^5+11 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+40 a^4 z^4+68 a^2 z^4+20 z^4 a^{-2} -2 z^4 a^{-4} +61 z^4+a^7 z^3-6 a^5 z^3-25 a^3 z^3-25 a z^3-3 z^3 a^{-1} +4 z^3 a^{-3} -3 a^6 z^2-14 a^4 z^2-24 a^2 z^2-6 z^2 a^{-2} -19 z^2+2 a^3 z+3 a z+z a^{-1} +a^4+2 a^2+2 }[/math] |
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