K12n327
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-5 q^{-1} +8 q^{-2} -9 q^{-3} +10 q^{-4} -9 q^{-5} +8 q^{-6} -5 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+9 t^2-11 t+11-11 t^{-1} +9 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+5 z^4+5 z^2+1 }[/math] |
| Determinant | 61 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^8-z^6 a^6-4 z^4 a^6-4 z^2 a^6-a^6+z^8 a^4+6 z^6 a^4+13 z^4 a^4+13 z^2 a^4+4 a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{11}-z a^{11}+2 z^4 a^{10}-z^2 a^{10}+4 z^5 a^9-5 z^3 a^9+3 z a^9+z^8 a^8-z^4 a^8+3 z^2 a^8-a^8+2 z^9 a^7-6 z^7 a^7+10 z^5 a^7-10 z^3 a^7+4 z a^7+z^{10} a^6+z^8 a^6-12 z^6 a^6+16 z^4 a^6-8 z^2 a^6+a^6+5 z^9 a^5-17 z^7 a^5+14 z^5 a^5-3 z^3 a^5-z a^5+z^{10} a^4+3 z^8 a^4-25 z^6 a^4+35 z^4 a^4-19 z^2 a^4+4 a^4+3 z^9 a^3-10 z^7 a^3+4 z^5 a^3+5 z^3 a^3-2 z a^3+3 z^8 a^2-13 z^6 a^2+16 z^4 a^2-7 z^2 a^2+a^2+z^7 a-4 z^5 a+4 z^3 a-z a }[/math] |
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