K12n610
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-5 q^3+8 q^2-10 q+11-10 q^{-1} +8 q^{-2} -5 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+8 t^2-12 t+15-12 t^{-1} +8 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+4 z^4+1 }[/math] |
| Determinant | 65 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-4 z^4 a^{-2} +12 z^4-4 a^2 z^2-4 z^2 a^{-2} +8 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+3 a z^9+4 z^9 a^{-1} +z^9 a^{-3} +4 a^2 z^8-3 z^8 a^{-2} +z^8+4 a^3 z^7-8 a z^7-15 z^7 a^{-1} -3 z^7 a^{-3} +3 a^4 z^6-10 a^2 z^6+5 z^6 a^{-2} +3 z^6 a^{-4} -11 z^6+a^5 z^5-9 a^3 z^5+8 a z^5+23 z^5 a^{-1} +6 z^5 a^{-3} +z^5 a^{-5} -7 a^4 z^4+9 a^2 z^4-2 z^4 a^{-2} -8 z^4 a^{-4} +22 z^4-2 a^5 z^3+4 a^3 z^3+2 a z^3-9 z^3 a^{-1} -8 z^3 a^{-3} -3 z^3 a^{-5} +2 a^4 z^2-3 a^2 z^2-z^2 a^{-2} +3 z^2 a^{-4} -9 z^2-a^3 z-2 a z+2 z a^{-3} +z a^{-5} +1 }[/math] |
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