K12n530
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 3 q^5-7 q^4+10 q^3-13 q^2+14 q-13+11 q^{-1} -7 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-10 t^2+19 t-21+19 t^{-1} -10 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+2 z^4-3 z^2+1 }[/math] |
| Determinant | 83 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-a^2 z^4+2 z^4 a^{-2} -z^4 a^{-4} +2 z^4-a^2 z^2-2 z^2 a^{-4} +a^2- a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+5 a z^9+9 z^9 a^{-1} +4 z^9 a^{-3} +4 a^2 z^8+2 z^8 a^{-4} +2 z^8+a^3 z^7-17 a z^7-30 z^7 a^{-1} -12 z^7 a^{-3} -15 a^2 z^6-13 z^6 a^{-2} -2 z^6 a^{-4} -26 z^6-3 a^3 z^5+13 a z^5+28 z^5 a^{-1} +15 z^5 a^{-3} +3 z^5 a^{-5} +15 a^2 z^4+14 z^4 a^{-2} +z^4 a^{-4} +28 z^4+2 a^3 z^3-2 a z^3-13 z^3 a^{-1} -7 z^3 a^{-3} +2 z^3 a^{-5} -3 a^2 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} +4 z^2 a^{-6} -8 z^2+a z+3 z a^{-1} -2 z a^{-5} -a^2- a^{-4} - a^{-6} }[/math] |
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