K12a698
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-12 q^2+22 q-31+38 q^{-1} -40 q^{-2} +37 q^{-3} -30 q^{-4} +20 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-28 t^2+55 t-67+55 t^{-1} -28 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^2+1 }[/math] |
| Determinant | 251 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-9 a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+8 a^4 z^2-11 a^2 z^2-z^2 a^{-2} +5 z^2-a^6+4 a^4-5 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+11 a^4 z^{10}+20 a^2 z^{10}+9 z^{10}+17 a^5 z^9+30 a^3 z^9+23 a z^9+10 z^9 a^{-1} +15 a^6 z^8+3 a^4 z^8-26 a^2 z^8+5 z^8 a^{-2} -9 z^8+9 a^7 z^7-26 a^5 z^7-88 a^3 z^7-80 a z^7-26 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-23 a^6 z^6-48 a^4 z^6-34 a^2 z^6-13 z^6 a^{-2} -26 z^6+a^9 z^5-10 a^7 z^5+16 a^5 z^5+77 a^3 z^5+72 a z^5+20 z^5 a^{-1} -2 z^5 a^{-3} -4 a^8 z^4+19 a^6 z^4+57 a^4 z^4+60 a^2 z^4+11 z^4 a^{-2} +37 z^4-a^9 z^3+5 a^7 z^3-a^5 z^3-28 a^3 z^3-27 a z^3-5 z^3 a^{-1} +z^3 a^{-3} +a^8 z^2-6 a^6 z^2-25 a^4 z^2-31 a^2 z^2-3 z^2 a^{-2} -16 z^2-a^7 z-a^5 z+3 a^3 z+4 a z+z a^{-1} +a^6+4 a^4+5 a^2+3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
