K12a198
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-19 q^3+27 q^2-32 q+33-30 q^{-1} +23 q^{-2} -15 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+16 t^2-50 t+73-50 t^{-1} +16 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+4 z^4-4 z^2+1 }[/math] |
| Determinant | 209 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-a^4+3 z^4 a^2+z^2 a^2-z^6+z^4+z^2+1-z^6 a^{-2} -z^4 a^{-2} -3 z^2 a^{-2} - a^{-2} +z^4 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+8 z^{10} a^{-2} +13 z^{10}+6 a^3 z^9+12 a z^9+19 z^9 a^{-1} +13 z^9 a^{-3} +5 a^4 z^8-a^2 z^8-3 z^8 a^{-2} +11 z^8 a^{-4} -20 z^8+3 a^5 z^7-7 a^3 z^7-33 a z^7-55 z^7 a^{-1} -27 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-8 a^4 z^6-7 a^2 z^6-22 z^6 a^{-2} -23 z^6 a^{-4} +z^6 a^{-6} +4 z^6-7 a^5 z^5+a^3 z^5+37 a z^5+53 z^5 a^{-1} +16 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+a^4 z^4+6 a^2 z^4+22 z^4 a^{-2} +11 z^4 a^{-4} -z^4 a^{-6} +12 z^4+5 a^5 z^3-2 a^3 z^3-20 a z^3-19 z^3 a^{-1} -5 z^3 a^{-3} +z^3 a^{-5} +3 a^6 z^2+3 a^4 z^2-3 a^2 z^2-6 z^2 a^{-2} -2 z^2 a^{-4} -7 z^2-a^5 z+2 a^3 z+4 a z+2 z a^{-1} +z a^{-3} -a^6-a^4+ a^{-2} + a^{-4} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
