K12a150
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+15 q^{-1} -21 q^{-2} +25 q^{-3} -24 q^{-4} +23 q^{-5} -17 q^{-6} +11 q^{-7} -6 q^{-8} +2 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-16 t^2+36 t-47+36 t^{-1} -16 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+8 z^4+8 z^2+1 }[/math] |
| Determinant | 159 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-3 a^8+z^6 a^6+3 z^4 a^6+5 z^2 a^6+2 a^6+2 z^6 a^4+6 z^4 a^4+8 z^2 a^4+4 a^4+z^6 a^2+z^4 a^2-z^2 a^2-2 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+8 z^3 a^{11}-4 z a^{11}+2 z^8 a^{10}-7 z^6 a^{10}+6 z^4 a^{10}+3 z^9 a^9-9 z^7 a^9+9 z^5 a^9-7 z^3 a^9+4 z a^9+3 z^{10} a^8-7 z^8 a^8+8 z^6 a^8-12 z^4 a^8+9 z^2 a^8-3 a^8+z^{11} a^7+7 z^9 a^7-29 z^7 a^7+46 z^5 a^7-42 z^3 a^7+14 z a^7+7 z^{10} a^6-11 z^8 a^6-z^6 a^6+11 z^4 a^6-7 z^2 a^6-2 a^6+z^{11} a^5+12 z^9 a^5-32 z^7 a^5+33 z^5 a^5-19 z^3 a^5+6 z a^5+4 z^{10} a^4+8 z^8 a^4-35 z^6 a^4+43 z^4 a^4-22 z^2 a^4+4 a^4+8 z^9 a^3-5 z^7 a^3-12 z^5 a^3+15 z^3 a^3-2 z a^3+10 z^8 a^2-15 z^6 a^2+9 z^4 a^2-5 z^2 a^2+2 a^2+8 z^7 a-12 z^5 a+6 z^3 a-2 z a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
