K12n571
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+2 q^3-3 q^2+4 q-3+4 q^{-1} -3 q^{-2} +2 q^{-3} -2 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+3 t^3-4 t^2+4 t-3+4 t^{-1} -4 t^{-2} +3 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-5 z^6-6 z^4-z^2+1 }[/math] |
| Determinant | 27 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8+a^2 z^6+z^6 a^{-2} -7 z^6+5 a^2 z^4+5 z^4 a^{-2} -16 z^4+6 a^2 z^2+6 z^2 a^{-2} -13 z^2+a^2+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+a z^9+3 z^9 a^{-1} +2 z^9 a^{-3} -5 z^8 a^{-2} +z^8 a^{-4} -6 z^8-5 a z^7-18 z^7 a^{-1} -13 z^7 a^{-3} +3 a^2 z^6+6 z^6 a^{-2} -6 z^6 a^{-4} +15 z^6+2 a^3 z^5+10 a z^5+34 z^5 a^{-1} +26 z^5 a^{-3} +2 a^4 z^4-9 a^2 z^4-2 z^4 a^{-2} +10 z^4 a^{-4} -23 z^4+2 a^5 z^3-2 a^3 z^3-11 a z^3-24 z^3 a^{-1} -17 z^3 a^{-3} +a^6 z^2-a^4 z^2+6 a^2 z^2+3 z^2 a^{-2} -4 z^2 a^{-4} +15 z^2-a^5 z-a^3 z+2 a z+4 z a^{-1} +2 z a^{-3} -a^2- a^{-2} -1 }[/math] |
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