K12a408
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-6 q^{11}+15 q^{10}-26 q^9+36 q^8-44 q^7+46 q^6-41 q^5+33 q^4-21 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+29 t^2-66 t+85-66 t^{-1} +29 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-z^4+5 z^2+1 }[/math] |
| Determinant | 285 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -6 z^4 a^{-6} +2 z^4 a^{-8} +z^4 a^{-10} +z^2 a^{-2} +4 z^2 a^{-4} -4 z^2 a^{-6} +5 z^2 a^{-8} -z^2 a^{-10} +2 a^{-4} - a^{-6} + a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-7} +4 z^{11} a^{-9} +11 z^{10} a^{-6} +25 z^{10} a^{-8} +14 z^{10} a^{-10} +13 z^9 a^{-5} +25 z^9 a^{-7} +32 z^9 a^{-9} +20 z^9 a^{-11} +9 z^8 a^{-4} -7 z^8 a^{-6} -36 z^8 a^{-8} -5 z^8 a^{-10} +15 z^8 a^{-12} +4 z^7 a^{-3} -24 z^7 a^{-5} -73 z^7 a^{-7} -85 z^7 a^{-9} -34 z^7 a^{-11} +6 z^7 a^{-13} +z^6 a^{-2} -17 z^6 a^{-4} -17 z^6 a^{-6} -4 z^6 a^{-8} -30 z^6 a^{-10} -24 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +21 z^5 a^{-5} +71 z^5 a^{-7} +62 z^5 a^{-9} +13 z^5 a^{-11} -6 z^5 a^{-13} -2 z^4 a^{-2} +14 z^4 a^{-4} +28 z^4 a^{-6} +24 z^4 a^{-8} +19 z^4 a^{-10} +7 z^4 a^{-12} +3 z^3 a^{-3} -10 z^3 a^{-5} -28 z^3 a^{-7} -17 z^3 a^{-9} -2 z^3 a^{-11} +z^2 a^{-2} -8 z^2 a^{-4} -13 z^2 a^{-6} -9 z^2 a^{-8} -4 z^2 a^{-10} +z^2 a^{-12} +z a^{-5} +5 z a^{-7} +3 z a^{-9} +z a^{-13} +2 a^{-4} + a^{-6} + a^{-8} + a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
