K12a430
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-10 q^{-1} +19 q^{-2} -26 q^{-3} +33 q^{-4} -35 q^{-5} +33 q^{-6} -27 q^{-7} +18 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+27 t^2-45 t+53-45 t^{-1} +27 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+7 z^4+5 z^2+1 }[/math] |
| Determinant | 221 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-3 z^2 a^8-a^8+z^8 a^6+4 z^6 a^6+6 z^4 a^6+3 z^2 a^6-a^6+z^8 a^4+4 z^6 a^4+7 z^4 a^4+8 z^2 a^4+4 a^4-z^6 a^2-3 z^4 a^2-3 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+9 z^7 a^{11}-12 z^5 a^{11}+8 z^3 a^{11}-2 z a^{11}+13 z^8 a^{10}-18 z^6 a^{10}+12 z^4 a^{10}-3 z^2 a^{10}+13 z^9 a^9-14 z^7 a^9+z^5 a^9+4 z^3 a^9+8 z^{10} a^8+5 z^8 a^8-31 z^6 a^8+22 z^4 a^8-2 z^2 a^8-a^8+2 z^{11} a^7+23 z^9 a^7-58 z^7 a^7+41 z^5 a^7-12 z^3 a^7+z a^7+14 z^{10} a^6-15 z^8 a^6-23 z^6 a^6+26 z^4 a^6-7 z^2 a^6+a^6+2 z^{11} a^5+17 z^9 a^5-53 z^7 a^5+39 z^5 a^5-7 z^3 a^5-2 z a^5+6 z^{10} a^4-3 z^8 a^4-26 z^6 a^4+33 z^4 a^4-15 z^2 a^4+4 a^4+7 z^9 a^3-17 z^7 a^3+9 z^5 a^3+3 z^3 a^3-2 z a^3+4 z^8 a^2-12 z^6 a^2+13 z^4 a^2-6 z^2 a^2+a^2+z^7 a-3 z^5 a+3 z^3 a-z a }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
