K12a404
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-4 q^4+9 q^3-14 q^2+20 q-23+24 q^{-1} -23 q^{-2} +18 q^{-3} -12 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-17 t^2+37 t-45+37 t^{-1} -17 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+z^4-4 z^2+1 }[/math] |
| Determinant | 159 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6+a^6-2 z^4 a^4-3 z^2 a^4+z^6 a^2-4 z^2 a^2-3 a^2+2 z^6+6 z^4+7 z^2+4-3 z^4 a^{-2} -6 z^2 a^{-2} -2 a^{-2} +z^2 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +7 a^2 z^{10}+5 z^{10} a^{-2} +12 z^{10}+11 a^3 z^9+14 a z^9+7 z^9 a^{-1} +4 z^9 a^{-3} +11 a^4 z^8-6 a^2 z^8-16 z^8 a^{-2} +z^8 a^{-4} -34 z^8+9 a^5 z^7-22 a^3 z^7-66 a z^7-52 z^7 a^{-1} -17 z^7 a^{-3} +6 a^6 z^6-18 a^4 z^6-27 a^2 z^6+5 z^6 a^{-2} -4 z^6 a^{-4} +6 z^6+3 a^7 z^5-12 a^5 z^5+11 a^3 z^5+76 a z^5+73 z^5 a^{-1} +23 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+8 a^4 z^4+37 a^2 z^4+19 z^4 a^{-2} +6 z^4 a^{-4} +35 z^4-2 a^7 z^3+8 a^5 z^3-4 a^3 z^3-37 a z^3-34 z^3 a^{-1} -11 z^3 a^{-3} -a^8 z^2+4 a^6 z^2-19 a^2 z^2-14 z^2 a^{-2} -4 z^2 a^{-4} -24 z^2-2 a^5 z+2 a^3 z+8 a z+6 z a^{-1} +2 z a^{-3} -a^6+3 a^2+2 a^{-2} + a^{-4} +4 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
