K12a201
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+9 q^2-14 q+20-23 q^{-1} +24 q^{-2} -22 q^{-3} +17 q^{-4} -12 q^{-5} +7 q^{-6} -3 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-37 t+53-37 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4-3 z^2+1 }[/math] |
| Determinant | 157 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-3 z^2 a^6-2 a^6+3 z^4 a^4+4 z^2 a^4+2 a^4-z^6 a^2-z^4 a^2-2 z^2 a^2-a^2-z^6-2 z^4-3 z^2+z^4 a^{-2} +z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^5 z^{11}+2 a^3 z^{11}+4 a^6 z^{10}+11 a^4 z^{10}+7 a^2 z^{10}+3 a^7 z^9+2 a^5 z^9+11 a^3 z^9+12 a z^9+a^8 z^8-15 a^6 z^8-36 a^4 z^8-6 a^2 z^8+14 z^8-14 a^7 z^7-33 a^5 z^7-52 a^3 z^7-20 a z^7+13 z^7 a^{-1} -5 a^8 z^6+12 a^6 z^6+25 a^4 z^6-21 a^2 z^6+9 z^6 a^{-2} -20 z^6+21 a^7 z^5+52 a^5 z^5+53 a^3 z^5+2 a z^5-16 z^5 a^{-1} +4 z^5 a^{-3} +8 a^8 z^4+6 a^6 z^4+9 a^4 z^4+22 a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} +2 z^4-13 a^7 z^3-25 a^5 z^3-14 a^3 z^3+4 a z^3+5 z^3 a^{-1} -z^3 a^{-3} -5 a^8 z^2-9 a^6 z^2-10 a^4 z^2-6 a^2 z^2+3 z^2 a^{-2} +3 z^2+3 a^7 z+3 a^5 z-a^3 z-2 a z-z a^{-1} +a^8+2 a^6+2 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. |
