K12a1268
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+19 q^2-27 q+33-35 q^{-1} +33 q^{-2} -26 q^{-3} +18 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+26 t^2-45 t+55-45 t^{-1} +26 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+6 z^4+z^2+1 }[/math] |
| Determinant | 221 |
| 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} +4 z^6-3 a^4 z^4+6 a^2 z^4-3 z^4 a^{-2} +6 z^4-3 a^4 z^2+4 a^2 z^2-3 z^2 a^{-2} +3 z^2-a^4+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+8 a^4 z^{10}+17 a^2 z^{10}+9 z^{10}+8 a^5 z^9+11 a^3 z^9+17 a z^9+14 z^9 a^{-1} +4 a^6 z^8-19 a^4 z^8-37 a^2 z^8+14 z^8 a^{-2} +a^7 z^7-25 a^5 z^7-48 a^3 z^7-49 a z^7-18 z^7 a^{-1} +9 z^7 a^{-3} -12 a^6 z^6+13 a^4 z^6+26 a^2 z^6-22 z^6 a^{-2} +4 z^6 a^{-4} -25 z^6-3 a^7 z^5+26 a^5 z^5+52 a^3 z^5+40 a z^5+5 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +10 a^6 z^4-7 a^4 z^4-16 a^2 z^4+17 z^4 a^{-2} -4 z^4 a^{-4} +22 z^4+2 a^7 z^3-12 a^5 z^3-27 a^3 z^3-17 a z^3+3 z^3 a^{-1} +6 z^3 a^{-3} -z^3 a^{-5} -2 a^6 z^2+5 a^4 z^2+8 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} -5 z^2+3 a^5 z+6 a^3 z+3 a z-z a^{-1} -z a^{-3} -a^4-2 a^2 }[/math] |
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