K12a858
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+9 q^2-14 q+20-24 q^{-1} +25 q^{-2} -23 q^{-3} +19 q^{-4} -13 q^{-5} +8 q^{-6} -4 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+16 t^2-38 t+51-38 t^{-1} +16 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-2 z^4-z^2+1 }[/math] |
| Determinant | 165 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^6+z^2 a^6-z^6 a^4-2 z^4 a^4-2 z^2 a^4-z^6 a^2+2 z^2 a^2+a^2-z^6-2 z^4-3 z^2-1+z^4 a^{-2} +z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+6 a^6 z^{10}+15 a^4 z^{10}+9 a^2 z^{10}+4 a^7 z^9-a^5 z^9+8 a^3 z^9+13 a z^9+a^8 z^8-26 a^6 z^8-58 a^4 z^8-17 a^2 z^8+14 z^8-18 a^7 z^7-35 a^5 z^7-54 a^3 z^7-24 a z^7+13 z^7 a^{-1} -4 a^8 z^6+33 a^6 z^6+66 a^4 z^6+a^2 z^6+9 z^6 a^{-2} -19 z^6+24 a^7 z^5+61 a^5 z^5+64 a^3 z^5+7 a z^5-16 z^5 a^{-1} +4 z^5 a^{-3} +4 a^8 z^4-13 a^6 z^4-24 a^4 z^4+a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} -z^4-11 a^7 z^3-29 a^5 z^3-24 a^3 z^3+5 z^3 a^{-1} -z^3 a^{-3} -a^8 z^2+2 a^4 z^2+3 a^2 z^2+3 z^2 a^{-2} +5 z^2+a^7 z+3 a^5 z+3 a^3 z-z a^{-1} -a^2- 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. |
