K12n739
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-3 q^{-1} +4 q^{-2} -3 q^{-3} +2 q^{-4} - q^{-5} + q^{-7} -2 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+5 t^2+t-5+ t^{-1} +5 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+z^4+z^2+1 }[/math] |
| Determinant | 13 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^2 a^8+a^8-z^6 a^6-6 z^4 a^6-8 z^2 a^6-3 a^6+z^8 a^4+6 z^6 a^4+11 z^4 a^4+9 z^2 a^4+2 a^4-z^6 a^2-4 z^4 a^2-2 z^2 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{10}-4 z^4 a^{10}+2 z^2 a^{10}+2 z^7 a^9-10 z^5 a^9+10 z^3 a^9-2 z a^9+z^8 a^8-6 z^6 a^8+7 z^4 a^8-3 z^2 a^8+a^8+z^7 a^7-9 z^5 a^7+12 z^3 a^7-4 z a^7+3 z^8 a^6-20 z^6 a^6+33 z^4 a^6-18 z^2 a^6+3 a^6+2 z^9 a^5-11 z^7 a^5+13 z^5 a^5-3 z^3 a^5-z a^5+5 z^8 a^4-28 z^6 a^4+41 z^4 a^4-19 z^2 a^4+2 a^4+2 z^9 a^3-9 z^7 a^3+8 z^5 a^3-2 z^3 a^3+z a^3+3 z^8 a^2-15 z^6 a^2+19 z^4 a^2-6 z^2 a^2-a^2+z^7 a-4 z^5 a+3 z^3 a }[/math] |
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