K12a523
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-10 q^5+17 q^4-25 q^3+32 q^2-33 q+32-26 q^{-1} +18 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+26 t^2-43 t+51-43 t^{-1} +26 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+6 z^4+3 z^2+1 }[/math] |
| Determinant | 213 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +4 z^6-3 a^2 z^4+6 z^4 a^{-2} -3 z^4 a^{-4} +6 z^4-3 a^2 z^2+5 z^2 a^{-2} -3 z^2 a^{-4} +4 z^2-a^2+3 a^{-2} -2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +6 z^{10} a^{-4} +7 z^{10}+12 a z^9+19 z^9 a^{-1} +14 z^9 a^{-3} +7 z^9 a^{-5} +13 a^2 z^8-16 z^8 a^{-2} -7 z^8 a^{-4} +4 z^8 a^{-6} +8 z^8+9 a^3 z^7-10 a z^7-44 z^7 a^{-1} -45 z^7 a^{-3} -19 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-19 a^2 z^6-13 z^6 a^{-2} -12 z^6 a^{-4} -12 z^6 a^{-6} -36 z^6+a^5 z^5-12 a^3 z^5-7 a z^5+24 z^5 a^{-1} +35 z^5 a^{-3} +14 z^5 a^{-5} -3 z^5 a^{-7} -4 a^4 z^4+14 a^2 z^4+14 z^4 a^{-2} +14 z^4 a^{-4} +11 z^4 a^{-6} +29 z^4-a^5 z^3+8 a^3 z^3+11 a z^3-4 z^3 a^{-1} -11 z^3 a^{-3} -2 z^3 a^{-5} +3 z^3 a^{-7} +a^4 z^2-5 a^2 z^2-3 z^2 a^{-6} -9 z^2-2 a^3 z-3 a z+3 z a^{-3} +z a^{-5} -z a^{-7} +a^2-3 a^{-2} -2 a^{-4} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
