K12a1178
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+12 q^2-18 q+23-25 q^{-1} +24 q^{-2} -20 q^{-3} +15 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+20 t^2-31 t+37-31 t^{-1} +20 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+6 z^4+1 }[/math] |
| Determinant | 161 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+4 a^2 z^6-z^6 a^{-2} +5 z^6-3 a^4 z^4+4 a^2 z^4-4 z^4 a^{-2} +9 z^4-2 a^4 z^2-4 z^2 a^{-2} +6 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+11 a^2 z^{10}+6 z^{10}+6 a^5 z^9+6 a^3 z^9+8 a z^9+8 z^9 a^{-1} +4 a^6 z^8-8 a^4 z^8-31 a^2 z^8+7 z^8 a^{-2} -12 z^8+a^7 z^7-16 a^5 z^7-29 a^3 z^7-38 a z^7-21 z^7 a^{-1} +5 z^7 a^{-3} -13 a^6 z^6-8 a^4 z^6+31 a^2 z^6-15 z^6 a^{-2} +3 z^6 a^{-4} +8 z^6-3 a^7 z^5+6 a^5 z^5+26 a^3 z^5+55 a z^5+28 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4+8 a^4 z^4-16 a^2 z^4+14 z^4 a^{-2} -6 z^4 a^{-4} +8 z^4+3 a^7 z^3+4 a^5 z^3-12 a^3 z^3-31 a z^3-12 z^3 a^{-1} +4 z^3 a^{-3} -2 z^3 a^{-5} -3 a^6 z^2+2 a^2 z^2-3 z^2 a^{-2} +2 z^2 a^{-4} -6 z^2-a^7 z-a^5 z+3 a^3 z+5 a z+2 z a^{-1} +1 }[/math] |
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