K12a1180
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-7 q^5+13 q^4-19 q^3+24 q^2-26 q+25-20 q^{-1} +15 q^{-2} -8 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+19 t^2-33 t+41-33 t^{-1} +19 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+11 z^4+3 z^2+1 }[/math] |
| Determinant | 165 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+5 z^6 a^{-2} -z^6 a^{-4} +5 z^6-4 a^2 z^4+9 z^4 a^{-2} -4 z^4 a^{-4} +10 z^4-6 a^2 z^2+5 z^2 a^{-2} -5 z^2 a^{-4} +9 z^2-2 a^2- a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +10 z^{10} a^{-2} +5 z^{10} a^{-4} +5 z^{10}+8 a z^9+6 z^9 a^{-1} +3 z^9 a^{-3} +5 z^9 a^{-5} +9 a^2 z^8-27 z^8 a^{-2} -16 z^8 a^{-4} +3 z^8 a^{-6} +z^8+6 a^3 z^7-9 a z^7-16 z^7 a^{-1} -20 z^7 a^{-3} -18 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-17 a^2 z^6+34 z^6 a^{-2} +23 z^6 a^{-4} -11 z^6 a^{-6} -20 z^6+a^5 z^5-8 a^3 z^5-2 a z^5+8 z^5 a^{-1} +28 z^5 a^{-3} +23 z^5 a^{-5} -4 z^5 a^{-7} -4 a^4 z^4+20 a^2 z^4-28 z^4 a^{-2} -23 z^4 a^{-4} +11 z^4 a^{-6} +30 z^4-2 a^5 z^3+4 a^3 z^3+11 a z^3+z^3 a^{-1} -23 z^3 a^{-3} -15 z^3 a^{-5} +4 z^3 a^{-7} +a^4 z^2-13 a^2 z^2+8 z^2 a^{-2} +9 z^2 a^{-4} -2 z^2 a^{-6} -17 z^2+a^5 z-a^3 z-4 a z+6 z a^{-3} +4 z a^{-5} +2 a^2- a^{-4} +4 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
