K12a1196
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+6 q^6-15 q^5+26 q^4-37 q^3+45 q^2-47 q+44-35 q^{-1} +23 q^{-2} -12 q^{-3} +5 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-13 t^3+36 t^2-61 t+73-61 t^{-1} +36 t^{-2} -13 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+3 z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 297 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+2 z^6 a^{-2} -z^6 a^{-4} +3 z^6-2 a^2 z^4-2 z^4 a^{-2} -z^4 a^{-4} +3 z^4-5 z^2 a^{-2} +2 z^2 a^{-4} +z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 6 z^{11} a^{-1} +6 z^{11} a^{-3} +33 z^{10} a^{-2} +15 z^{10} a^{-4} +18 z^{10}+24 a z^9+31 z^9 a^{-1} +21 z^9 a^{-3} +14 z^9 a^{-5} +20 a^2 z^8-70 z^8 a^{-2} -29 z^8 a^{-4} +6 z^8 a^{-6} -15 z^8+12 a^3 z^7-38 a z^7-104 z^7 a^{-1} -90 z^7 a^{-3} -35 z^7 a^{-5} +z^7 a^{-7} +5 a^4 z^6-26 a^2 z^6+22 z^6 a^{-2} +2 z^6 a^{-4} -12 z^6 a^{-6} -23 z^6+a^5 z^5-11 a^3 z^5+20 a z^5+86 z^5 a^{-1} +78 z^5 a^{-3} +23 z^5 a^{-5} -z^5 a^{-7} -3 a^4 z^4+10 a^2 z^4+22 z^4 a^{-2} +13 z^4 a^{-4} +5 z^4 a^{-6} +27 z^4+2 a^3 z^3-a z^3-19 z^3 a^{-1} -18 z^3 a^{-3} -2 z^3 a^{-5} +a^2 z^2-13 z^2 a^{-2} -6 z^2 a^{-4} +z^2 a^{-6} -5 z^2-a z-z a^{-1} -z a^{-3} -z a^{-5} -a^2+ a^{-2} + a^{-4} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
