K12a810
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+5 q^9-11 q^8+19 q^7-29 q^6+35 q^5-38 q^4+37 q^3-29 q^2+21 q-12+5 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-23 t^2+57 t-75+57 t^{-1} -23 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+z^4+z^2+1 }[/math] |
| Determinant | 243 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +3 z^4 a^{-4} -z^4 a^{-8} -z^4+3 z^2 a^{-4} -2 z^2 a^{-6} + a^{-2} +2 a^{-4} -3 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +10 z^{10} a^{-4} +19 z^{10} a^{-6} +9 z^{10} a^{-8} +17 z^9 a^{-3} +25 z^9 a^{-5} +18 z^9 a^{-7} +10 z^9 a^{-9} +18 z^8 a^{-2} +7 z^8 a^{-4} -33 z^8 a^{-6} -17 z^8 a^{-8} +5 z^8 a^{-10} +12 z^7 a^{-1} -19 z^7 a^{-3} -70 z^7 a^{-5} -71 z^7 a^{-7} -31 z^7 a^{-9} +z^7 a^{-11} -26 z^6 a^{-2} -46 z^6 a^{-4} -5 z^6 a^{-6} -4 z^6 a^{-8} -14 z^6 a^{-10} +5 z^6+a z^5-13 z^5 a^{-1} +54 z^5 a^{-5} +71 z^5 a^{-7} +29 z^5 a^{-9} -2 z^5 a^{-11} +13 z^4 a^{-2} +36 z^4 a^{-4} +28 z^4 a^{-6} +17 z^4 a^{-8} +9 z^4 a^{-10} -3 z^4+3 z^3 a^{-1} +z^3 a^{-3} -14 z^3 a^{-5} -19 z^3 a^{-7} -7 z^3 a^{-9} -2 z^2 a^{-2} -9 z^2 a^{-4} -12 z^2 a^{-6} -5 z^2 a^{-8} +z a^{-3} -z a^{-5} -4 z a^{-7} -2 z a^{-9} - a^{-2} +2 a^{-4} +3 a^{-6} + a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
