K12a595
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+8 q^5-13 q^4+18 q^3-20 q^2+21 q-19+15 q^{-1} -10 q^{-2} +6 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+33 t-43+33 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4-z^2+1 }[/math] |
| Determinant | 139 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-2 a^2 z^4+z^4 a^{-2} -2 z^4 a^{-4} +2 z^4+a^4 z^2-4 a^2 z^2-2 z^2 a^{-4} +z^2 a^{-6} +3 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+4 z^{10} a^{-2} +7 z^{10}+3 a^3 z^9+6 a z^9+11 z^9 a^{-1} +8 z^9 a^{-3} +a^4 z^8-10 a^2 z^8+4 z^8 a^{-2} +11 z^8 a^{-4} -18 z^8-15 a^3 z^7-39 a z^7-42 z^7 a^{-1} -7 z^7 a^{-3} +11 z^7 a^{-5} -5 a^4 z^6+2 a^2 z^6-30 z^6 a^{-2} -14 z^6 a^{-4} +8 z^6 a^{-6} -z^6+24 a^3 z^5+60 a z^5+43 z^5 a^{-1} -10 z^5 a^{-3} -13 z^5 a^{-5} +4 z^5 a^{-7} +8 a^4 z^4+17 a^2 z^4+24 z^4 a^{-2} +z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +24 z^4-14 a^3 z^3-33 a z^3-20 z^3 a^{-1} +5 z^3 a^{-3} +4 z^3 a^{-5} -2 z^3 a^{-7} -5 a^4 z^2-13 a^2 z^2-6 z^2 a^{-2} +2 z^2 a^{-4} +2 z^2 a^{-6} -14 z^2+3 a^3 z+6 a z+4 z a^{-1} +z a^{-3} +a^4+2 a^2+2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
