K12a496
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-22 q^6+32 q^5-40 q^4+43 q^3-39 q^2+33 q-22+12 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-32 t^2+55 t-65+55 t^{-1} -32 t^{-2} +12 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-4 z^6+3 z^2+1 }[/math] |
| Determinant | 267 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -3 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +z^6-2 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4 a^{-6} +2 z^4+2 z^2 a^{-2} +z^2 a^{-4} +3 a^{-2} - a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +19 z^{10} a^{-4} +10 z^{10} a^{-6} +13 z^9 a^{-1} +24 z^9 a^{-3} +25 z^9 a^{-5} +14 z^9 a^{-7} +7 z^8 a^{-2} -15 z^8 a^{-4} +11 z^8 a^{-8} +11 z^8+5 a z^7-15 z^7 a^{-1} -48 z^7 a^{-3} -55 z^7 a^{-5} -22 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-40 z^6 a^{-2} -25 z^6 a^{-4} -27 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -20 z^6-8 a z^5-5 z^5 a^{-1} +14 z^5 a^{-3} +26 z^5 a^{-5} +7 z^5 a^{-7} -8 z^5 a^{-9} -a^2 z^4+28 z^4 a^{-2} +24 z^4 a^{-4} +22 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +13 z^4+4 a z^3+9 z^3 a^{-1} +8 z^3 a^{-3} +5 z^3 a^{-5} +5 z^3 a^{-7} +3 z^3 a^{-9} -3 z^2 a^{-2} -5 z^2 a^{-4} -5 z^2 a^{-6} -z^2 a^{-8} -2 z^2-z a^{-1} -2 z a^{-3} -4 z a^{-5} -3 z a^{-7} -3 a^{-2} + 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. |
