K12a248
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+8 q^2-13 q+19-21 q^{-1} +22 q^{-2} -20 q^{-3} +16 q^{-4} -11 q^{-5} +6 q^{-6} -3 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-34 t+47-34 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4+1 }[/math] |
| Determinant | 145 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-3 z^2 a^6-3 a^6+3 z^4 a^4+5 z^2 a^4+3 a^4-z^6 a^2-z^4 a^2-z^2 a^2-a^2-z^6-2 z^4-2 z^2+1+z^4 a^{-2} +z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+3 a^6 z^{10}+8 a^4 z^{10}+5 a^2 z^{10}+3 a^7 z^9+8 a^5 z^9+15 a^3 z^9+10 a z^9+a^8 z^8-9 a^6 z^8-20 a^4 z^8+2 a^2 z^8+12 z^8-15 a^7 z^7-49 a^5 z^7-61 a^3 z^7-16 a z^7+11 z^7 a^{-1} -5 a^8 z^6-2 a^6 z^6-7 a^4 z^6-35 a^2 z^6+8 z^6 a^{-2} -17 z^6+25 a^7 z^5+77 a^5 z^5+71 a^3 z^5+3 a z^5-12 z^5 a^{-1} +4 z^5 a^{-3} +8 a^8 z^4+22 a^6 z^4+39 a^4 z^4+36 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +3 z^4-17 a^7 z^3-46 a^5 z^3-35 a^3 z^3-2 a z^3+2 z^3 a^{-1} -2 z^3 a^{-3} -5 a^8 z^2-17 a^6 z^2-23 a^4 z^2-12 a^2 z^2+2 z^2 a^{-2} +z^2+4 a^7 z+10 a^5 z+8 a^3 z+2 a z+a^8+3 a^6+3 a^4+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. |
