K12a302
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-7+13 q^{-1} -17 q^{-2} +22 q^{-3} -23 q^{-4} +21 q^{-5} -17 q^{-6} +12 q^{-7} -7 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-16 t^2+33 t-41+33 t^{-1} -16 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 147 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+2 z^4 a^6+z^2 a^6+2 z^6 a^4+6 z^4 a^4+6 z^2 a^4+a^4+z^6 a^2+2 z^4 a^2+2 z^2 a^2+2 a^2-z^4-2 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-11 z^6 a^{10}+12 z^4 a^{10}-4 z^2 a^{10}+4 z^9 a^9-11 z^7 a^9+5 z^5 a^9+3 z^3 a^9-z a^9+3 z^{10} a^8-3 z^8 a^8-9 z^6 a^8+8 z^4 a^8+z^2 a^8-a^8+z^{11} a^7+6 z^9 a^7-18 z^7 a^7+8 z^5 a^7+2 z^3 a^7-z a^7+6 z^{10} a^6-8 z^8 a^6-2 z^6 a^6+z^4 a^6+z^2 a^6+z^{11} a^5+7 z^9 a^5-12 z^7 a^5-z^5 a^5+8 z^3 a^5-3 z a^5+3 z^{10} a^4+4 z^8 a^4-13 z^6 a^4+11 z^4 a^4-5 z^2 a^4+a^4+5 z^9 a^3-z^7 a^3-7 z^5 a^3+7 z^3 a^3-z a^3+6 z^8 a^2-6 z^6 a^2+z^4 a^2+2 z^2 a^2-2 a^2+5 z^7 a-6 z^5 a+z^3 a+z a+3 z^6-5 z^4+3 z^2-1+z^5 a^{-1} -2 z^3 a^{-1} +z a^{-1} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
