K12a25
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+11 q^4-17 q^3+24 q^2-28 q+29-26 q^{-1} +20 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-44 t+63-44 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4-2 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-2 a^4+3 z^4 a^2+3 z^2 a^2+2 a^2-z^6-z^2-1-z^6 a^{-2} -z^4 a^{-2} -z^2 a^{-2} + a^{-2} +z^4 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+5 z^{10} a^{-2} +8 z^{10}+4 a^3 z^9+11 a z^9+17 z^9 a^{-1} +10 z^9 a^{-3} +4 a^4 z^8+4 a^2 z^8+7 z^8 a^{-2} +10 z^8 a^{-4} -3 z^8+3 a^5 z^7-22 a z^7-41 z^7 a^{-1} -17 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-5 a^4 z^6-11 a^2 z^6-37 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -19 z^6-8 a^5 z^5-12 a^3 z^5+16 a z^5+31 z^5 a^{-1} +2 z^5 a^{-3} -9 z^5 a^{-5} -3 a^6 z^4-4 a^4 z^4+3 a^2 z^4+32 z^4 a^{-2} +11 z^4 a^{-4} -z^4 a^{-6} +24 z^4+7 a^5 z^3+10 a^3 z^3-4 a z^3-6 z^3 a^{-1} +3 z^3 a^{-3} +2 z^3 a^{-5} +3 a^6 z^2+7 a^4 z^2+3 a^2 z^2-6 z^2 a^{-2} -z^2 a^{-4} -6 z^2-2 a^5 z-2 a^3 z-a^6-2 a^4-2 a^2- a^{-2} -1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
