K12a202
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-12 q^3+22 q^2-32 q+40-42 q^{-1} +39 q^{-2} -32 q^{-3} +22 q^{-4} -12 q^{-5} +5 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+28 t^2-58 t+75-58 t^{-1} +28 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^2+1 }[/math] |
| Determinant | 265 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-8 a^2 z^4-2 z^4 a^{-2} +7 z^4-a^6 z^2+4 a^4 z^2-7 a^2 z^2-z^2 a^{-2} +3 z^2+a^4-a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+9 a^4 z^{10}+21 a^2 z^{10}+12 z^{10}+10 a^5 z^9+25 a^3 z^9+35 a z^9+20 z^9 a^{-1} +5 a^6 z^8-8 a^4 z^8-24 a^2 z^8+19 z^8 a^{-2} +8 z^8+a^7 z^7-26 a^5 z^7-85 a^3 z^7-96 a z^7-26 z^7 a^{-1} +12 z^7 a^{-3} -13 a^6 z^6-28 a^4 z^6-43 a^2 z^6-26 z^6 a^{-2} +5 z^6 a^{-4} -59 z^6-2 a^7 z^5+21 a^5 z^5+76 a^3 z^5+73 a z^5+7 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+39 a^4 z^4+64 a^2 z^4+13 z^4 a^{-2} -3 z^4 a^{-4} +52 z^4+a^7 z^3-6 a^5 z^3-24 a^3 z^3-19 a z^3+z^3 a^{-1} +3 z^3 a^{-3} -3 a^6 z^2-15 a^4 z^2-22 a^2 z^2-2 z^2 a^{-2} -12 z^2+2 a^3 z+2 a z+a^4+a^2- a^{-2} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
