K12n456
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+q^5-q^4+q^3+q^2-2 q+4-4 q^{-1} +4 q^{-2} -3 q^{-3} +2 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-5 t+9-5 t^{-1} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+6 z^4+4 z^2+1 }[/math] |
| Determinant | 17 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +a^2 z^4+6 z^4 a^{-2} -z^4 a^{-4} -a^4 z^2+2 a^2 z^2+10 z^2 a^{-2} -4 z^2 a^{-4} -3 z^2-a^4+2 a^2+6 a^{-2} -3 a^{-4} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +2 z^9 a^{-3} +z^9 a^{-5} +a^2 z^8-9 z^8 a^{-2} -8 z^8 a^{-4} +2 a^3 z^7+2 a z^7-9 z^7 a^{-1} -17 z^7 a^{-3} -8 z^7 a^{-5} +2 a^4 z^6-2 a^2 z^6+26 z^6 a^{-2} +21 z^6 a^{-4} +z^6+a^5 z^5-6 a^3 z^5-7 a z^5+24 z^5 a^{-1} +45 z^5 a^{-3} +21 z^5 a^{-5} -6 a^4 z^4-a^2 z^4-32 z^4 a^{-2} -23 z^4 a^{-4} -4 z^4-3 a^5 z^3+4 a^3 z^3+9 a z^3-21 z^3 a^{-1} -44 z^3 a^{-3} -21 z^3 a^{-5} +3 a^4 z^2+4 a^2 z^2+20 z^2 a^{-2} +12 z^2 a^{-4} +9 z^2+a^5 z-a^3 z-2 a z+6 z a^{-1} +13 z a^{-3} +7 z a^{-5} -a^4-2 a^2-6 a^{-2} -3 a^{-4} -3 }[/math] |
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