K12n619
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-7 q^{-1} +11 q^{-2} -13 q^{-3} +14 q^{-4} -13 q^{-5} +11 q^{-6} -7 q^{-7} +3 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+14 t^2-15 t+13-15 t^{-1} +14 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^6-2 z^4+3 z^2+1 }[/math] |
| Determinant | 85 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+z^4 a^8+5 z^2 a^8+3 a^8-2 z^6 a^6-9 z^4 a^6-11 z^2 a^6-5 a^6+z^8 a^4+5 z^6 a^4+9 z^4 a^4+10 z^2 a^4+4 a^4-z^6 a^2-3 z^4 a^2-z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{11}-z a^{11}+3 z^4 a^{10}-3 z^2 a^{10}+a^{10}+z^7 a^9+z^5 a^9+z a^9+4 z^8 a^8-13 z^6 a^8+22 z^4 a^8-13 z^2 a^8+3 a^8+5 z^9 a^7-17 z^7 a^7+23 z^5 a^7-13 z^3 a^7+3 z a^7+2 z^{10} a^6+3 z^8 a^6-31 z^6 a^6+47 z^4 a^6-27 z^2 a^6+5 a^6+10 z^9 a^5-36 z^7 a^5+38 z^5 a^5-17 z^3 a^5+2 z a^5+2 z^{10} a^4+3 z^8 a^4-33 z^6 a^4+43 z^4 a^4-21 z^2 a^4+4 a^4+5 z^9 a^3-17 z^7 a^3+13 z^5 a^3-3 z^3 a^3+z a^3+4 z^8 a^2-15 z^6 a^2+15 z^4 a^2-4 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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