K12n425
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-4 q^{-1} +5 q^{-2} -5 q^{-3} +6 q^{-4} -4 q^{-5} +3 q^{-6} -2 q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+7 t^2-4 t+1-4 t^{-1} +7 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+3 z^4+4 z^2+1 }[/math] |
| Determinant | 33 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-z^6 a^6-5 z^4 a^6-6 z^2 a^6-3 a^6+z^8 a^4+6 z^6 a^4+12 z^4 a^4+12 z^2 a^4+5 a^4-z^6 a^2-4 z^4 a^2-3 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^6 z^{10}+a^4 z^{10}+a^7 z^9+4 a^5 z^9+3 a^3 z^9-3 a^6 z^8+3 a^2 z^8-5 a^7 z^7-19 a^5 z^7-13 a^3 z^7+a z^7-5 a^6 z^6-19 a^4 z^6-14 a^2 z^6+6 a^7 z^5+20 a^5 z^5+10 a^3 z^5-4 a z^5+18 a^6 z^4+34 a^4 z^4+16 a^2 z^4-a^9 z^3-a^7 z^3+a^5 z^3+4 a^3 z^3+3 a z^3-a^8 z^2-15 a^6 z^2-20 a^4 z^2-6 a^2 z^2+2 a^9 z-a^7 z-5 a^5 z-3 a^3 z-a z+3 a^6+5 a^4+a^2 }[/math] |
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