K12n721
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+q^2-2 q+4-3 q^{-1} +4 q^{-2} -3 q^{-3} +3 q^{-4} -2 q^{-5} + q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-2 t^3+3 t^2-4 t+5-4 t^{-1} +3 t^{-2} -2 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+6 z^6+11 z^4+6 z^2+1 }[/math] |
| Determinant | 25 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8-a^4 z^6+8 a^2 z^6-z^6-6 a^4 z^4+23 a^2 z^4-6 z^4-11 a^4 z^2+28 a^2 z^2-11 z^2-6 a^4+12 a^2-5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+a^5 z^9+2 a^3 z^9+a z^9+a^6 z^8-7 a^4 z^8-8 a^2 z^8+a^7 z^7-5 a^5 z^7-13 a^3 z^7-7 a z^7-5 a^6 z^6+20 a^4 z^6+27 a^2 z^6+2 z^6-6 a^7 z^5+7 a^5 z^5+32 a^3 z^5+20 a z^5+z^5 a^{-1} +6 a^6 z^4-30 a^4 z^4-45 a^2 z^4+z^4 a^{-2} -8 z^4+10 a^7 z^3-4 a^5 z^3-36 a^3 z^3-24 a z^3-z^3 a^{-1} +z^3 a^{-3} -a^6 z^2+20 a^4 z^2+36 a^2 z^2-z^2 a^{-2} +14 z^2-4 a^7 z+a^5 z+13 a^3 z+11 a z+z a^{-1} -2 z a^{-3} -6 a^4-12 a^2-5 }[/math] |
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