K12a1130
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+11 q^2-15 q+18-19 q^{-1} +18 q^{-2} -14 q^{-3} +10 q^{-4} -6 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+16 t^2-23 t+27-23 t^{-1} +16 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+8 z^4+z^2+1 }[/math] |
| Determinant | 125 |
| 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+8 a^2 z^4-4 z^4 a^{-2} +8 z^4-4 a^4 z^2+5 a^2 z^2-4 z^2 a^{-2} +4 z^2-a^4+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+4 a^5 z^9+4 a^3 z^9+5 a z^9+5 z^9 a^{-1} +3 a^6 z^8-7 a^4 z^8-18 a^2 z^8+6 z^8 a^{-2} -2 z^8+a^7 z^7-14 a^5 z^7-20 a^3 z^7-19 a z^7-9 z^7 a^{-1} +5 z^7 a^{-3} -12 a^6 z^6+a^4 z^6+25 a^2 z^6-13 z^6 a^{-2} +3 z^6 a^{-4} -4 z^6-4 a^7 z^5+12 a^5 z^5+24 a^3 z^5+27 a z^5+8 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +13 a^6 z^4-22 a^2 z^4+13 z^4 a^{-2} -6 z^4 a^{-4} +10 z^4+4 a^7 z^3-2 a^5 z^3-14 a^3 z^3-16 a z^3+6 z^3 a^{-3} -2 z^3 a^{-5} -4 a^6 z^2+3 a^4 z^2+9 a^2 z^2-4 z^2 a^{-2} +2 z^2 a^{-4} -4 z^2-a^7 z+3 a^3 z+2 a z-z a^{-1} -z a^{-3} -a^4-2 a^2 }[/math] |
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