K12n805
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^6-4 q^5+7 q^4-11 q^3+13 q^2-14 q+13-10 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+8 t^2-19 t+27-19 t^{-1} +8 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-4 z^4-5 z^2+1 }[/math] |
| Determinant | 85 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+a^2 z^4-3 z^4 a^{-2} +z^4 a^{-4} -3 z^4+2 a^2 z^2-4 z^2 a^{-2} +z^2 a^{-4} -4 z^2+2 a^2- a^{-2} + a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +4 z^9 a^{-1} +5 z^9 a^{-3} +z^9 a^{-5} +5 z^8 a^{-2} -z^8 a^{-4} +6 z^8+7 a z^7-6 z^7 a^{-1} -14 z^7 a^{-3} -z^7 a^{-5} +6 a^2 z^6-16 z^6 a^{-2} +3 z^6 a^{-6} -7 z^6+3 a^3 z^5-9 a z^5+8 z^5 a^{-1} +15 z^5 a^{-3} -5 z^5 a^{-5} +a^4 z^4-8 a^2 z^4+14 z^4 a^{-2} -6 z^4 a^{-4} -11 z^4 a^{-6} -2 a^3 z^3+4 a z^3-12 z^3 a^{-1} -11 z^3 a^{-3} +7 z^3 a^{-5} -a^4 z^2+6 a^2 z^2-8 z^2 a^{-2} +5 z^2 a^{-4} +10 z^2 a^{-6} +4 z^2+a z+5 z a^{-1} +2 z a^{-3} -2 z a^{-5} -2 a^2+ a^{-2} - a^{-6} -1 }[/math] |
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