K12a655
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+14 q-19+24 q^{-1} -24 q^{-2} +23 q^{-3} -18 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-17 t^2+36 t-45+36 t^{-1} -17 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+7 z^4+4 z^2+1 }[/math] |
| Determinant | 159 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+2 z^4 a^4+z^2 a^4-a^4+2 z^6 a^2+6 z^4 a^2+8 z^2 a^2+5 a^2+z^6+z^4-2 z^2-2-z^4 a^{-2} -z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+11 a^2 z^{10}+6 z^{10}+6 a^5 z^9+6 a^3 z^9+7 a z^9+7 z^9 a^{-1} +6 a^6 z^8-7 a^4 z^8-33 a^2 z^8+4 z^8 a^{-2} -16 z^8+5 a^7 z^7-7 a^5 z^7-27 a^3 z^7-40 a z^7-24 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-7 a^6 z^6+6 a^4 z^6+37 a^2 z^6-13 z^6 a^{-2} +8 z^6+a^9 z^5-7 a^7 z^5+3 a^5 z^5+36 a^3 z^5+51 a z^5+23 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+3 a^6 z^4-4 a^4 z^4-24 a^2 z^4+10 z^4 a^{-2} -2 z^4-2 a^9 z^3+3 a^7 z^3-21 a^3 z^3-28 a z^3-10 z^3 a^{-1} +2 z^3 a^{-3} +2 a^8 z^2-2 a^6 z^2+3 a^4 z^2+13 a^2 z^2-2 z^2 a^{-2} +4 z^2+a^9 z-a^7 z+6 a^3 z+7 a z+3 z a^{-1} +a^6-a^4-5 a^2-2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
