K12a620
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-12 q^9+22 q^8-33 q^7+40 q^6-43 q^5+40 q^4-32 q^3+23 q^2-12 q+5- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+33 t^2-55 t+65-55 t^{-1} +33 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+4 z^6+z^4+z^2+1 }[/math] |
| Determinant | 269 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +3 z^6 a^{-4} +3 z^6 a^{-6} -z^6 a^{-8} -2 z^4 a^{-2} +3 z^4 a^{-4} +2 z^4 a^{-6} -2 z^4 a^{-8} +3 z^2 a^{-4} -2 z^2 a^{-6} + a^{-2} +2 a^{-4} -3 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-5} +4 z^{11} a^{-7} +10 z^{10} a^{-4} +24 z^{10} a^{-6} +14 z^{10} a^{-8} +10 z^9 a^{-3} +19 z^9 a^{-5} +30 z^9 a^{-7} +21 z^9 a^{-9} +5 z^8 a^{-2} -14 z^8 a^{-4} -42 z^8 a^{-6} -4 z^8 a^{-8} +19 z^8 a^{-10} +z^7 a^{-1} -25 z^7 a^{-3} -70 z^7 a^{-5} -86 z^7 a^{-7} -30 z^7 a^{-9} +12 z^7 a^{-11} -13 z^6 a^{-2} -13 z^6 a^{-4} -2 z^6 a^{-6} -32 z^6 a^{-8} -25 z^6 a^{-10} +5 z^6 a^{-12} -2 z^5 a^{-1} +18 z^5 a^{-3} +58 z^5 a^{-5} +62 z^5 a^{-7} +11 z^5 a^{-9} -12 z^5 a^{-11} +z^5 a^{-13} +11 z^4 a^{-2} +22 z^4 a^{-4} +25 z^4 a^{-6} +27 z^4 a^{-8} +10 z^4 a^{-10} -3 z^4 a^{-12} +z^3 a^{-1} -4 z^3 a^{-3} -14 z^3 a^{-5} -9 z^3 a^{-7} +3 z^3 a^{-9} +3 z^3 a^{-11} -2 z^2 a^{-2} -9 z^2 a^{-4} -12 z^2 a^{-6} -5 z^2 a^{-8} +z a^{-3} -z a^{-5} -4 z a^{-7} -2 z a^{-9} - a^{-2} +2 a^{-4} +3 a^{-6} + a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
