K12n515
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+8 q^8-12 q^7+14 q^6-15 q^5+14 q^4-10 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+10 t^2-20 t+25-20 t^{-1} +10 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-2 z^4+2 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -2 z^4 a^{-4} -2 z^4 a^{-6} +z^4 a^{-8} +2 z^2 a^{-2} -z^2 a^{-6} +z^2 a^{-8} + a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +3 z^9 a^{-5} +5 z^9 a^{-7} +2 z^9 a^{-9} +4 z^8 a^{-4} +5 z^8 a^{-6} +2 z^8 a^{-8} +z^8 a^{-10} +3 z^7 a^{-3} -2 z^7 a^{-5} -8 z^7 a^{-7} -3 z^7 a^{-9} +z^6 a^{-2} -8 z^6 a^{-4} -13 z^6 a^{-6} -2 z^6 a^{-8} +2 z^6 a^{-10} -8 z^5 a^{-3} -7 z^5 a^{-5} +7 z^5 a^{-7} +10 z^5 a^{-9} +4 z^5 a^{-11} -3 z^4 a^{-2} +z^4 a^{-4} +7 z^4 a^{-6} +2 z^4 a^{-8} +z^4 a^{-12} +5 z^3 a^{-3} +4 z^3 a^{-5} -6 z^3 a^{-7} -9 z^3 a^{-9} -4 z^3 a^{-11} +3 z^2 a^{-2} +z^2 a^{-4} -3 z^2 a^{-6} -z^2 a^{-8} -z^2 a^{-10} -z^2 a^{-12} -z a^{-5} +z a^{-7} +3 z a^{-9} +z a^{-11} - a^{-2} + a^{-4} + a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
