K12a500
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-8 q^6+14 q^5-20 q^4+24 q^3-26 q^2+24 q-19+14 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-21 t^2+35 t-39+35 t^{-1} -21 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+z^4-2 z^2+1 }[/math] |
| Determinant | 167 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-11 z^4 a^{-2} +7 z^4 a^{-4} -z^4 a^{-6} +7 z^4-2 a^2 z^2-12 z^2 a^{-2} +7 z^2 a^{-4} -2 z^2 a^{-6} +7 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +4 z^{10} a^{-4} +4 z^{10}+6 a z^9+13 z^9 a^{-1} +14 z^9 a^{-3} +7 z^9 a^{-5} +4 a^2 z^8-8 z^8 a^{-2} +6 z^8 a^{-4} +8 z^8 a^{-6} -2 z^8+a^3 z^7-19 a z^7-48 z^7 a^{-1} -39 z^7 a^{-3} -4 z^7 a^{-5} +7 z^7 a^{-7} -14 a^2 z^6-26 z^6 a^{-2} -26 z^6 a^{-4} -8 z^6 a^{-6} +4 z^6 a^{-8} -26 z^6-3 a^3 z^5+16 a z^5+50 z^5 a^{-1} +34 z^5 a^{-3} -8 z^5 a^{-5} -10 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+46 z^4 a^{-2} +26 z^4 a^{-4} -2 z^4 a^{-6} -6 z^4 a^{-8} +38 z^4+2 a^3 z^3-5 a z^3-19 z^3 a^{-1} -7 z^3 a^{-3} +10 z^3 a^{-5} +4 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2-24 z^2 a^{-2} -10 z^2 a^{-4} +3 z^2 a^{-6} +2 z^2 a^{-8} -18 z^2+a z+2 z a^{-1} -2 z a^{-3} -4 z a^{-5} -z a^{-7} +4 a^{-2} +2 a^{-4} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
