K12a1170
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+13 q^2-18 q+23-24 q^{-1} +22 q^{-2} -18 q^{-3} +13 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+18 t^2-30 t+37-30 t^{-1} +18 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+10 z^4+2 z^2+1 }[/math] |
| Determinant | 153 |
| 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} +9 z^4-5 a^4 z^2+6 a^2 z^2-5 z^2 a^{-2} +6 z^2-a^4+a^2- a^{-2} +2 }[/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+a^3 z^9+6 a z^9+9 z^9 a^{-1} +3 a^6 z^8-9 a^4 z^8-32 a^2 z^8+9 z^8 a^{-2} -11 z^8+a^7 z^7-10 a^5 z^7-11 a^3 z^7-30 a z^7-24 z^7 a^{-1} +6 z^7 a^{-3} -11 a^6 z^6+5 a^4 z^6+46 a^2 z^6-24 z^6 a^{-2} +3 z^6 a^{-4} +3 z^6-4 a^7 z^5+a^5 z^5+8 a^3 z^5+45 a z^5+29 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +12 a^6 z^4-8 a^4 z^4-38 a^2 z^4+29 z^4 a^{-2} -5 z^4 a^{-4} +16 z^4+5 a^7 z^3+7 a^5 z^3-7 a^3 z^3-27 a z^3-9 z^3 a^{-1} +7 z^3 a^{-3} -2 z^3 a^{-5} -4 a^6 z^2+6 a^4 z^2+11 a^2 z^2-12 z^2 a^{-2} -11 z^2-2 a^7 z-2 a^5 z+3 a^3 z+5 a z+z a^{-1} -z a^{-3} -a^4-a^2+ a^{-2} +2 }[/math] |
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