K12a271
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+16 q^2-23 q+28-29 q^{-1} +27 q^{-2} -21 q^{-3} +15 q^{-4} -8 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-39 t+47-39 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +5 z^6+3 a^4 z^4-11 a^2 z^4-3 z^4 a^{-2} +11 z^4-a^6 z^2+8 a^4 z^2-13 a^2 z^2-3 z^2 a^{-2} +11 z^2-2 a^6+5 a^4-5 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+9 a^2 z^{10}+5 z^{10}+5 a^5 z^9+15 a^3 z^9+20 a z^9+10 z^9 a^{-1} +3 a^6 z^8-2 a^4 z^8-5 a^2 z^8+11 z^8 a^{-2} +11 z^8+a^7 z^7-14 a^5 z^7-51 a^3 z^7-55 a z^7-11 z^7 a^{-1} +8 z^7 a^{-3} -10 a^6 z^6-20 a^4 z^6-36 a^2 z^6-17 z^6 a^{-2} +4 z^6 a^{-4} -47 z^6-4 a^7 z^5+11 a^5 z^5+55 a^3 z^5+52 a z^5-11 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+29 a^4 z^4+53 a^2 z^4+12 z^4 a^{-2} -5 z^4 a^{-4} +52 z^4+5 a^7 z^3-3 a^5 z^3-28 a^3 z^3-21 a z^3+5 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} -6 a^6 z^2-18 a^4 z^2-28 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} -22 z^2-2 a^7 z+5 a^3 z+3 a z-z a^{-1} -z a^{-3} +2 a^6+5 a^4+5 a^2+ a^{-2} +4 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
