K12a1140
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+4 q^6-7 q^5+10 q^4-13 q^3+14 q^2-14 q+13-9 q^{-1} +6 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+11 t^2-21 t+27-21 t^{-1} +11 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-7 z^4-4 z^2+1 }[/math] |
| Determinant | 97 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-2 z^4 a^{-2} -4 z^4 a^{-4} +z^4 a^{-6} -3 z^4+2 a^2 z^2-6 z^2 a^{-4} +3 z^2 a^{-6} -3 z^2+a^2+ a^{-2} -3 a^{-4} +2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +5 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-1} +2 z^9 a^{-3} -z^9 a^{-5} +2 z^9 a^{-7} -6 z^8 a^{-2} -22 z^8 a^{-4} -9 z^8 a^{-6} +z^8 a^{-8} +6 z^8+6 a z^7-11 z^7 a^{-1} -15 z^7 a^{-3} -9 z^7 a^{-5} -11 z^7 a^{-7} +5 a^2 z^6+4 z^6 a^{-2} +37 z^6 a^{-4} +12 z^6 a^{-6} -6 z^6 a^{-8} -10 z^6+3 a^3 z^5-8 a z^5+10 z^5 a^{-1} +19 z^5 a^{-3} +17 z^5 a^{-5} +19 z^5 a^{-7} +a^4 z^4-6 a^2 z^4-6 z^4 a^{-2} -37 z^4 a^{-4} -8 z^4 a^{-6} +11 z^4 a^{-8} +5 z^4-3 a^3 z^3+4 a z^3-5 z^3 a^{-1} -11 z^3 a^{-3} -11 z^3 a^{-5} -12 z^3 a^{-7} -a^4 z^2+3 a^2 z^2+4 z^2 a^{-2} +18 z^2 a^{-4} +6 z^2 a^{-6} -6 z^2 a^{-8} +2 z^2+z a^{-1} +z a^{-3} +3 z a^{-5} +3 z a^{-7} -a^2- a^{-2} -3 a^{-4} -2 a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
