K12a1238
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-6 q^6+11 q^5-16 q^4+19 q^3-20 q^2+19 q-15+11 q^{-1} -6 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+9 t^3-16 t^2+23 t-25+23 t^{-1} -16 t^{-2} +9 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+12 z^6+8 z^4+z^2+1 }[/math] |
| Determinant | 131 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +8 z^8 a^{-2} -z^8 a^{-4} -z^8+24 z^6 a^{-2} -6 z^6 a^{-4} -6 z^6+32 z^4 a^{-2} -12 z^4 a^{-4} -12 z^4+17 z^2 a^{-2} -8 z^2 a^{-4} -8 z^2+2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +9 z^{10} a^{-2} +5 z^{10} a^{-4} +4 z^{10}+4 a z^9-2 z^9 a^{-1} +6 z^9 a^{-5} +3 a^2 z^8-37 z^8 a^{-2} -15 z^8 a^{-4} +6 z^8 a^{-6} -13 z^8+a^3 z^7-13 a z^7-7 z^7 a^{-1} -12 z^7 a^{-3} -14 z^7 a^{-5} +5 z^7 a^{-7} -12 a^2 z^6+68 z^6 a^{-2} +27 z^6 a^{-4} -12 z^6 a^{-6} +3 z^6 a^{-8} +14 z^6-4 a^3 z^5+8 a z^5+12 z^5 a^{-1} +27 z^5 a^{-3} +16 z^5 a^{-5} -10 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4-62 z^4 a^{-2} -22 z^4 a^{-4} +9 z^4 a^{-6} -6 z^4 a^{-8} -12 z^4+4 a^3 z^3+2 a z^3-10 z^3 a^{-1} -20 z^3 a^{-3} -4 z^3 a^{-5} +6 z^3 a^{-7} -2 z^3 a^{-9} -4 a^2 z^2+21 z^2 a^{-2} +9 z^2 a^{-4} +2 z^2 a^{-8} +6 z^2-a^3 z-a z+2 z a^{-1} +3 z a^{-3} -z a^{-7} -2 a^{-2} - a^{-4} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
