K12a371
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-5 q^{-1} +8 q^{-2} -11 q^{-3} +14 q^{-4} -14 q^{-5} +14 q^{-6} -11 q^{-7} +8 q^{-8} -5 q^{-9} +2 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+14 t^2-17 t+17-17 t^{-1} +14 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+12 z^4+8 z^2+1 }[/math] |
| Determinant | 97 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-5 z^4 a^8-8 z^2 a^8-5 a^8+z^8 a^6+6 z^6 a^6+14 z^4 a^6+17 z^2 a^6+8 a^6+z^8 a^4+5 z^6 a^4+7 z^4 a^4+2 z^2 a^4-2 a^4-z^6 a^2-4 z^4 a^2-3 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-3 z^3 a^{13}+2 z a^{13}+2 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+3 z^7 a^{11}-6 z^5 a^{11}+4 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-5 z^6 a^{10}+4 z^4 a^{10}-2 z^2 a^{10}+3 z^9 a^9-7 z^7 a^9+10 z^5 a^9-5 z^3 a^9+z a^9+3 z^{10} a^8-12 z^8 a^8+29 z^6 a^8-35 z^4 a^8+23 z^2 a^8-5 a^8+z^{11} a^7+2 z^9 a^7-20 z^7 a^7+46 z^5 a^7-39 z^3 a^7+11 z a^7+6 z^{10} a^6-28 z^8 a^6+55 z^6 a^6-57 z^4 a^6+32 z^2 a^6-8 a^6+z^{11} a^5+3 z^9 a^5-28 z^7 a^5+53 z^5 a^5-40 z^3 a^5+9 z a^5+3 z^{10} a^4-10 z^8 a^4+6 z^6 a^4+2 z^2 a^4-2 a^4+4 z^9 a^3-17 z^7 a^3+20 z^5 a^3-10 z^3 a^3+3 z a^3+3 z^8 a^2-13 z^6 a^2+14 z^4 a^2-4 z^2 a^2+z^7 a-4 z^5 a+3 z^3 a }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
