K12a482
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+4 q^4-7 q^3+11 q^2-13 q+14-14 q^{-1} +11 q^{-2} -8 q^{-3} +5 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-23 t+39-23 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4-7 z^2+1 }[/math] |
| Determinant | 93 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-2 z^2 a^4+z^4 a^2-2 z^2 a^2-a^2+2 z^4+z^4 a^{-2} -z^2 a^{-2} + a^{-2} -2 z^2 a^{-4} - a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+2 z^{10} a^{-2} +4 z^{10}+3 a^3 z^9-a z^9-2 z^9 a^{-1} +2 z^9 a^{-3} +3 a^4 z^8-4 a^2 z^8-7 z^8 a^{-2} +2 z^8 a^{-4} -16 z^8+2 a^5 z^7-9 a^3 z^7-2 a z^7+3 z^7 a^{-1} -4 z^7 a^{-3} +2 z^7 a^{-5} +a^6 z^6-9 a^4 z^6+15 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +30 z^6-6 a^5 z^5+11 a^3 z^5+9 a z^5+z^5 a^{-3} -7 z^5 a^{-5} -4 a^6 z^4+7 a^4 z^4+9 a^2 z^4-15 z^4 a^{-2} -2 z^4 a^{-4} -4 z^4 a^{-6} -19 z^4+3 a^5 z^3-10 a^3 z^3-6 a z^3+2 z^3 a^{-1} +z^3 a^{-3} +6 z^3 a^{-5} +4 a^6 z^2-3 a^4 z^2-8 a^2 z^2+5 z^2 a^{-2} +4 z^2 a^{-4} +4 z^2 a^{-6} +4 z^2+4 a^3 z+2 a z-2 z a^{-1} -z a^{-3} -z a^{-5} -a^6+a^2- a^{-2} - a^{-4} - a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
