K12n591
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{12}+q^{11}-2 q^{10}+2 q^9-q^8+q^7+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-2 t^2+2 t-1+2 t^{-1} -2 t^{-2} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+8 z^6+18 z^4+10 z^2+1 }[/math] |
| Determinant | 7 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +8 z^6 a^{-8} +20 z^4 a^{-8} -z^4 a^{-10} -z^4 a^{-12} +17 z^2 a^{-8} -3 z^2 a^{-10} -4 z^2 a^{-12} +4 a^{-8} - a^{-10} -3 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^8 a^{-8} -z^8 a^{-12} -z^7 a^{-11} -z^7 a^{-13} -8 z^6 a^{-8} -z^6 a^{-10} +7 z^6 a^{-12} -z^5 a^{-9} +6 z^5 a^{-11} +7 z^5 a^{-13} +20 z^4 a^{-8} +5 z^4 a^{-10} -14 z^4 a^{-12} +z^4 a^{-14} +4 z^3 a^{-9} -8 z^3 a^{-11} -11 z^3 a^{-13} +z^3 a^{-15} -17 z^2 a^{-8} -5 z^2 a^{-10} +12 z^2 a^{-12} -3 z a^{-9} +3 z a^{-11} +5 z a^{-13} -z a^{-15} +4 a^{-8} + a^{-10} -3 a^{-12} - a^{-14} }[/math] |
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