K13a1563
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a1563/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-37 t^2+71 t-87+71 t^{-1} -37 t^{-2} +12 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1563/Conway Polynomial |
| Determinant | 331 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-4 a^4 z^6-3 a^2 z^6+2 z^6+3 a^6 z^4-8 a^4 z^4-5 a^2 z^4-z^4 a^{-2} +6 z^4+4 a^6 z^2-6 a^4 z^2-5 a^2 z^2-2 z^2 a^{-2} +8 z^2+a^6-a^4-2 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^{12}+2 a^2 z^{12}+8 a^5 z^{11}+14 a^3 z^{11}+6 a z^{11}+14 a^6 z^{10}+24 a^4 z^{10}+18 a^2 z^{10}+8 z^{10}+14 a^7 z^9+7 a^5 z^9-10 a^3 z^9+4 a z^9+7 z^9 a^{-1} +9 a^8 z^8-22 a^6 z^8-60 a^4 z^8-41 a^2 z^8+4 z^8 a^{-2} -8 z^8+4 a^9 z^7-28 a^7 z^7-44 a^5 z^7-27 a^3 z^7-31 a z^7-15 z^7 a^{-1} +z^7 a^{-3} +a^{10} z^6-16 a^8 z^6+15 a^6 z^6+56 a^4 z^6+17 a^2 z^6-12 z^6 a^{-2} -19 z^6-7 a^9 z^5+28 a^7 z^5+57 a^5 z^5+38 a^3 z^5+25 a z^5+6 z^5 a^{-1} -3 z^5 a^{-3} -2 a^{10} z^4+10 a^8 z^4-6 a^6 z^4-28 a^4 z^4+10 a^2 z^4+13 z^4 a^{-2} +33 z^4+3 a^9 z^3-17 a^7 z^3-33 a^5 z^3-21 a^3 z^3-7 a z^3+4 z^3 a^{-1} +3 z^3 a^{-3} +a^{10} z^2-3 a^8 z^2+3 a^6 z^2+9 a^4 z^2-11 a^2 z^2-6 z^2 a^{-2} -19 z^2+4 a^7 z+8 a^5 z+5 a^3 z-2 z a^{-1} -z a^{-3} -a^6-a^4+2 a^2+ a^{-2} +4 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
