K12a1169
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+11 q^2-16 q+20-21 q^{-1} +20 q^{-2} -16 q^{-3} +12 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+17 t^2-26 t+31-26 t^{-1} +17 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+9 z^4+2 z^2+1 }[/math] |
| Determinant | 137 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+5 a^2 z^6-z^6 a^{-2} +5 z^6-4 a^4 z^4+9 a^2 z^4-4 z^4 a^{-2} +8 z^4-5 a^4 z^2+8 a^2 z^2-4 z^2 a^{-2} +3 z^2-2 a^4+4 a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+4 a^4 z^{10}+10 a^2 z^{10}+6 z^{10}+4 a^5 z^9+4 a z^9+8 z^9 a^{-1} +3 a^6 z^8-11 a^4 z^8-39 a^2 z^8+7 z^8 a^{-2} -18 z^8+a^7 z^7-11 a^5 z^7-14 a^3 z^7-33 a z^7-26 z^7 a^{-1} +5 z^7 a^{-3} -11 a^6 z^6+10 a^4 z^6+64 a^2 z^6-18 z^6 a^{-2} +3 z^6 a^{-4} +22 z^6-4 a^7 z^5+3 a^5 z^5+20 a^3 z^5+61 a z^5+37 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4-15 a^4 z^4-55 a^2 z^4+18 z^4 a^{-2} -6 z^4 a^{-4} -5 z^4+5 a^7 z^3+4 a^5 z^3-17 a^3 z^3-39 a z^3-17 z^3 a^{-1} +4 z^3 a^{-3} -2 z^3 a^{-5} -3 a^6 z^2+11 a^4 z^2+22 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +2 z^2-2 a^7 z-a^5 z+5 a^3 z+7 a z+3 z a^{-1} -2 a^4-4 a^2-1 }[/math] |
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