K12a485
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+6 q^3-14 q^2+23 q-32+39 q^{-1} -40 q^{-2} +37 q^{-3} -29 q^{-4} +19 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-28 t^2+56 t-69+56 t^{-1} -28 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-z^8 }[/math] |
| Determinant | 255 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-8 a^2 z^4-z^4 a^{-2} +4 z^4-2 a^6 z^2+7 a^4 z^2-6 a^2 z^2+z^2-a^6+2 a^4+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^3 z^{11}+4 a z^{11}+11 a^4 z^{10}+23 a^2 z^{10}+12 z^{10}+15 a^5 z^9+22 a^3 z^9+20 a z^9+13 z^9 a^{-1} +14 a^6 z^8-a^4 z^8-43 a^2 z^8+6 z^8 a^{-2} -22 z^8+9 a^7 z^7-17 a^5 z^7-65 a^3 z^7-75 a z^7-35 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-20 a^6 z^6-32 a^4 z^6+a^2 z^6-13 z^6 a^{-2} -4 z^6+a^9 z^5-11 a^7 z^5+43 a^3 z^5+55 a z^5+23 z^5 a^{-1} -z^5 a^{-3} -4 a^8 z^4+15 a^6 z^4+35 a^4 z^4+23 a^2 z^4+5 z^4 a^{-2} +12 z^4-a^9 z^3+7 a^7 z^3+10 a^5 z^3-2 a^3 z^3-3 a z^3+z^3 a^{-1} +a^8 z^2-5 a^6 z^2-14 a^4 z^2-9 a^2 z^2+2 z^2 a^{-2} +z^2-2 a^7 z-4 a^5 z-4 a^3 z-4 a z-2 z a^{-1} +a^6+2 a^4- 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. |
