K13a2821
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Polynomial invariants
| Jones polynomial | Data:K13a2821/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+26 t^2-32 t+33-32 t^{-1} +26 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a2821/Conway Polynomial |
| Determinant | 177 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -2 z^6 a^{-2} +3 z^6 a^{-4} +4 z^6 a^{-6} -z^6 a^{-8} -8 z^4 a^{-2} -z^4 a^{-4} +5 z^4 a^{-6} -3 z^4 a^{-8} +z^4-7 z^2 a^{-2} -5 z^2 a^{-4} +5 z^2 a^{-6} -z^2 a^{-8} +4 z^2-2 a^{-2} -2 a^{-4} +2 a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-4} +z^{12} a^{-6} +3 z^{11} a^{-3} +7 z^{11} a^{-5} +4 z^{11} a^{-7} +3 z^{10} a^{-2} +5 z^{10} a^{-4} +9 z^{10} a^{-6} +7 z^{10} a^{-8} +2 z^9 a^{-1} -11 z^9 a^{-3} -25 z^9 a^{-5} -4 z^9 a^{-7} +8 z^9 a^{-9} -12 z^8 a^{-2} -37 z^8 a^{-4} -46 z^8 a^{-6} -14 z^8 a^{-8} +8 z^8 a^{-10} +z^8-9 z^7 a^{-1} +13 z^7 a^{-3} +29 z^7 a^{-5} -10 z^7 a^{-7} -10 z^7 a^{-9} +7 z^7 a^{-11} +11 z^6 a^{-2} +70 z^6 a^{-4} +78 z^6 a^{-6} +13 z^6 a^{-8} -8 z^6 a^{-10} +4 z^6 a^{-12} -6 z^6+10 z^5 a^{-1} -17 z^5 a^{-3} -15 z^5 a^{-5} +21 z^5 a^{-7} -2 z^5 a^{-9} -10 z^5 a^{-11} +z^5 a^{-13} -64 z^4 a^{-4} -58 z^4 a^{-6} -5 z^4 a^{-8} -5 z^4 a^{-10} -6 z^4 a^{-12} +12 z^4-z^3 a^{-1} +18 z^3 a^{-3} +6 z^3 a^{-5} -8 z^3 a^{-7} +9 z^3 a^{-9} +3 z^3 a^{-11} -z^3 a^{-13} -4 z^2 a^{-2} +25 z^2 a^{-4} +17 z^2 a^{-6} +z^2 a^{-8} +5 z^2 a^{-10} +2 z^2 a^{-12} -10 z^2-2 z a^{-1} -6 z a^{-3} -3 z a^{-5} -z a^{-7} -3 z a^{-9} -z a^{-11} +2 a^{-2} -2 a^{-4} -2 a^{-6} +3 }[/math] |
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