K12a770
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-18 q^6+25 q^5-30 q^4+32 q^3-29 q^2+23 q-15+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-17 t^2+48 t-65+48 t^{-1} -17 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-5 z^4-2 z^2+1 }[/math] |
| Determinant | 199 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} -z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2+z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-8} -2 z^2+a^2+2 a^{-2} -2 a^{-4} + a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +12 z^{10} a^{-4} +7 z^{10} a^{-6} +6 z^9 a^{-1} +10 z^9 a^{-3} +14 z^9 a^{-5} +10 z^9 a^{-7} -2 z^8 a^{-2} -21 z^8 a^{-4} -6 z^8 a^{-6} +8 z^8 a^{-8} +5 z^8+3 a z^7-7 z^7 a^{-1} -25 z^7 a^{-3} -39 z^7 a^{-5} -20 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-3 z^6 a^{-2} +20 z^6 a^{-4} -3 z^6 a^{-6} -16 z^6 a^{-8} +z^6 a^{-10} -8 z^6-7 a z^5+25 z^5 a^{-3} +42 z^5 a^{-5} +16 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4-2 z^4 a^{-2} -18 z^4 a^{-4} -z^4 a^{-6} +9 z^4 a^{-8} -2 z^4 a^{-10} +z^4+5 a z^3+z^3 a^{-1} -14 z^3 a^{-3} -25 z^3 a^{-5} -11 z^3 a^{-7} +4 z^3 a^{-9} +3 a^2 z^2+5 z^2 a^{-2} +11 z^2 a^{-4} +3 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} +3 z^2-a z+4 z a^{-3} +6 z a^{-5} +3 z a^{-7} -a^2-2 a^{-2} -2 a^{-4} - a^{-6} -1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
