K12a707
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-13 q^3+24 q^2-34 q+41-43 q^{-1} +40 q^{-2} -31 q^{-3} +21 q^{-4} -11 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+29 t^2-59 t+75-59 t^{-1} +29 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^4+z^2+1 }[/math] |
| Determinant | 269 |
| 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+5 a^4 z^2-7 a^2 z^2-2 z^2 a^{-2} +6 z^2-a^6+2 a^4-a^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+8 a^4 z^{10}+21 a^2 z^{10}+13 z^{10}+8 a^5 z^9+22 a^3 z^9+37 a z^9+23 z^9 a^{-1} +4 a^6 z^8-8 a^4 z^8-25 a^2 z^8+22 z^8 a^{-2} +9 z^8+a^7 z^7-20 a^5 z^7-74 a^3 z^7-98 a z^7-32 z^7 a^{-1} +13 z^7 a^{-3} -11 a^6 z^6-18 a^4 z^6-32 a^2 z^6-32 z^6 a^{-2} +5 z^6 a^{-4} -62 z^6-3 a^7 z^5+17 a^5 z^5+70 a^3 z^5+75 a z^5+12 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+28 a^4 z^4+47 a^2 z^4+19 z^4 a^{-2} -2 z^4 a^{-4} +51 z^4+3 a^7 z^3-6 a^5 z^3-28 a^3 z^3-26 a z^3-3 z^3 a^{-1} +4 z^3 a^{-3} -5 a^6 z^2-12 a^4 z^2-16 a^2 z^2-5 z^2 a^{-2} -14 z^2-a^7 z+a^5 z+5 a^3 z+4 a z+z a^{-1} +a^6+2 a^4+a^2+1 }[/math] |
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