K12n690
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+8 q^2-9 q+9-6 q^{-1} +5 q^{-2} - q^{-3} - q^{-4} + q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3+2 t^2-12 t+19-12 t^{-1} +2 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 45 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6-a^4 z^4+6 a^2 z^4+z^4 a^{-2} +2 z^4-4 a^4 z^2+8 a^2 z^2-z^2 a^{-2} -z^2 a^{-4} +3 z^2-3 a^4+4 a^2-2 a^{-2} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+a^5 z^9+2 a^3 z^9+2 a z^9+z^9 a^{-1} -8 a^4 z^8-8 a^2 z^8+4 z^8 a^{-2} +4 z^8-8 a^5 z^7-19 a^3 z^7-13 a z^7+3 z^7 a^{-1} +5 z^7 a^{-3} +19 a^4 z^6+18 a^2 z^6-10 z^6 a^{-2} +3 z^6 a^{-4} -14 z^6+21 a^5 z^5+53 a^3 z^5+33 a z^5-13 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} -17 a^4 z^4-9 a^2 z^4+10 z^4 a^{-2} -6 z^4 a^{-4} +24 z^4-23 a^5 z^3-53 a^3 z^3-27 a z^3+15 z^3 a^{-1} +10 z^3 a^{-3} -2 z^3 a^{-5} +7 a^4 z^2+2 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} -13 z^2+9 a^5 z+17 a^3 z+8 a z-4 z a^{-1} -4 z a^{-3} -3 a^4-4 a^2+2 a^{-2} +2 }[/math] |
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