K12a479
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-12 q^3+22 q^2-32 q+39-41 q^{-1} +38 q^{-2} -30 q^{-3} +21 q^{-4} -11 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+28 t^2-56 t+71-56 t^{-1} +28 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+1 }[/math] |
| Determinant | 257 |
| 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} +7 z^4-a^6 z^2+5 a^4 z^2-6 a^2 z^2-z^2 a^{-2} +3 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}+20 a^2 z^{10}+12 z^{10}+8 a^5 z^9+20 a^3 z^9+32 a z^9+20 z^9 a^{-1} +4 a^6 z^8-9 a^4 z^8-27 a^2 z^8+19 z^8 a^{-2} +5 z^8+a^7 z^7-20 a^5 z^7-69 a^3 z^7-87 a z^7-27 z^7 a^{-1} +12 z^7 a^{-3} -11 a^6 z^6-16 a^4 z^6-23 a^2 z^6-26 z^6 a^{-2} +5 z^6 a^{-4} -49 z^6-3 a^7 z^5+16 a^5 z^5+62 a^3 z^5+64 a z^5+8 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+24 a^4 z^4+37 a^2 z^4+12 z^4 a^{-2} -3 z^4 a^{-4} +39 z^4+3 a^7 z^3-5 a^5 z^3-21 a^3 z^3-14 a z^3+2 z^3 a^{-1} +3 z^3 a^{-3} -5 a^6 z^2-11 a^4 z^2-10 a^2 z^2-z^2 a^{-2} -5 z^2-a^7 z+2 a^3 z-z a^{-1} +a^6+2 a^4- a^{-2} -1 }[/math] |
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