K12n641
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-5 q^{-1} +9 q^{-2} -10 q^{-3} +11 q^{-4} -11 q^{-5} +9 q^{-6} -6 q^{-7} +3 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+9 t^2-13 t+15-13 t^{-1} +9 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+5 z^4+3 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4 z^8-a^6 z^6+6 a^4 z^6-a^2 z^6-4 a^6 z^4+13 a^4 z^4-4 a^2 z^4-5 a^6 z^2+12 a^4 z^2-4 a^2 z^2-2 a^6+3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{11}-z a^{11}+3 z^4 a^{10}-2 z^2 a^{10}+z^7 a^9+3 z^3 a^9-z a^9+2 z^8 a^8-3 z^6 a^8+4 z^4 a^8+2 z^9 a^7-2 z^7 a^7-3 z^5 a^7+5 z^3 a^7-z a^7+z^{10} a^6+2 z^8 a^6-11 z^6 a^6+10 z^4 a^6-6 z^2 a^6+2 a^6+5 z^9 a^5-14 z^7 a^5+8 z^5 a^5-2 z^3 a^5+z^{10} a^4+3 z^8 a^4-21 z^6 a^4+26 z^4 a^4-15 z^2 a^4+3 a^4+3 z^9 a^3-10 z^7 a^3+7 z^5 a^3-z^3 a^3+z a^3+3 z^8 a^2-13 z^6 a^2+17 z^4 a^2-7 z^2 a^2+z^7 a-4 z^5 a+4 z^3 a }[/math] |
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