K12a163
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-10 q^8+19 q^7-28 q^6+34 q^5-37 q^4+35 q^3-28 q^2+20 q-10+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-22 t^2+54 t-71+54 t^{-1} -22 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +3 z^6 a^{-4} +9 z^4 a^{-4} -6 z^4 a^{-6} -z^4-z^2 a^{-2} +12 z^2 a^{-4} -12 z^2 a^{-6} +4 z^2 a^{-8} -z^2+5 a^{-4} -7 a^{-6} +4 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +9 z^{10} a^{-4} +15 z^{10} a^{-6} +6 z^{10} a^{-8} +16 z^9 a^{-3} +29 z^9 a^{-5} +20 z^9 a^{-7} +7 z^9 a^{-9} +15 z^8 a^{-2} +9 z^8 a^{-4} -11 z^8 a^{-6} -z^8 a^{-8} +4 z^8 a^{-10} +9 z^7 a^{-1} -25 z^7 a^{-3} -80 z^7 a^{-5} -64 z^7 a^{-7} -17 z^7 a^{-9} +z^7 a^{-11} -25 z^6 a^{-2} -59 z^6 a^{-4} -51 z^6 a^{-6} -33 z^6 a^{-8} -12 z^6 a^{-10} +4 z^6+a z^5-10 z^5 a^{-1} +17 z^5 a^{-3} +70 z^5 a^{-5} +56 z^5 a^{-7} +11 z^5 a^{-9} -3 z^5 a^{-11} +23 z^4 a^{-2} +71 z^4 a^{-4} +75 z^4 a^{-6} +44 z^4 a^{-8} +13 z^4 a^{-10} -4 z^4-a z^3+4 z^3 a^{-1} -6 z^3 a^{-3} -29 z^3 a^{-5} -22 z^3 a^{-7} -z^3 a^{-9} +3 z^3 a^{-11} -9 z^2 a^{-2} -34 z^2 a^{-4} -40 z^2 a^{-6} -22 z^2 a^{-8} -6 z^2 a^{-10} +z^2+3 z a^{-3} +6 z a^{-5} +4 z a^{-7} -z a^{-11} +5 a^{-4} +7 a^{-6} +4 a^{-8} + a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
