K12a258
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-13 q^3+19 q^2-24 q+27-25 q^{-1} +21 q^{-2} -15 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+20 t^2-35 t+43-35 t^{-1} +20 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-7 a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} +11 z^4+2 a^4 z^2-8 a^2 z^2-11 z^2 a^{-2} +3 z^2 a^{-4} +12 z^2+a^4-3 a^2-5 a^{-2} +2 a^{-4} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+3 z^{10} a^{-2} +7 z^{10}+7 a^3 z^9+12 a z^9+10 z^9 a^{-1} +5 z^9 a^{-3} +7 a^4 z^8+4 a^2 z^8+5 z^8 a^{-2} +5 z^8 a^{-4} -3 z^8+4 a^5 z^7-10 a^3 z^7-28 a z^7-24 z^7 a^{-1} -7 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-15 a^4 z^6-25 a^2 z^6-26 z^6 a^{-2} -12 z^6 a^{-4} +z^6 a^{-6} -22 z^6-9 a^5 z^5-3 a^3 z^5+19 a z^5+20 z^5 a^{-1} -z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+8 a^4 z^4+27 a^2 z^4+36 z^4 a^{-2} +10 z^4 a^{-4} -3 z^4 a^{-6} +40 z^4+5 a^5 z^3+6 a^3 z^3-2 z^3 a^{-1} +5 z^3 a^{-3} +6 z^3 a^{-5} +a^6 z^2-3 a^4 z^2-14 a^2 z^2-22 z^2 a^{-2} -6 z^2 a^{-4} +2 z^2 a^{-6} -24 z^2-a^5 z-2 a^3 z-2 a z-2 z a^{-1} -3 z a^{-3} -2 z a^{-5} +a^4+3 a^2+5 a^{-2} +2 a^{-4} +6 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
