K12a1204
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-7 q^3+13 q^2-18 q+22-23 q^{-1} +22 q^{-2} -17 q^{-3} +12 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+18 t^2-29 t+35-29 t^{-1} +18 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+10 z^4+3 z^2+1 }[/math] |
| Determinant | 149 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+5 a^2 z^6-z^6 a^{-2} +5 z^6-4 a^4 z^4+9 a^2 z^4-4 z^4 a^{-2} +9 z^4-5 a^4 z^2+7 a^2 z^2-5 z^2 a^{-2} +6 z^2-2 a^4+3 a^2- a^{-2} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+4 a^4 z^{10}+10 a^2 z^{10}+6 z^{10}+4 a^5 z^9+5 a z^9+9 z^9 a^{-1} +3 a^6 z^8-11 a^4 z^8-36 a^2 z^8+9 z^8 a^{-2} -13 z^8+a^7 z^7-11 a^5 z^7-10 a^3 z^7-29 a z^7-25 z^7 a^{-1} +6 z^7 a^{-3} -11 a^6 z^6+13 a^4 z^6+62 a^2 z^6-24 z^6 a^{-2} +3 z^6 a^{-4} +11 z^6-4 a^7 z^5+4 a^5 z^5+15 a^3 z^5+52 a z^5+32 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4-19 a^4 z^4-58 a^2 z^4+28 z^4 a^{-2} -5 z^4 a^{-4} +5 z^4+5 a^7 z^3+4 a^5 z^3-19 a^3 z^3-39 a z^3-12 z^3 a^{-1} +7 z^3 a^{-3} -2 z^3 a^{-5} -2 a^6 z^2+13 a^4 z^2+20 a^2 z^2-10 z^2 a^{-2} -5 z^2-2 a^7 z+7 a^3 z+8 a z+2 z a^{-1} -z a^{-3} -2 a^4-3 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. |
