K13a4540
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Polynomial invariants
| Jones polynomial | Data:K13a4540/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+22 t^2-44 t+53-44 t^{-1} +22 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | Data:K13a4540/Conway Polynomial |
| Determinant | 193 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{12}-a^{12}+2 z^4 a^{10}+3 z^2 a^{10}-z^6 a^8+3 z^2 a^8+a^8-2 z^6 a^6-4 z^4 a^6-z^2 a^6-z^6 a^4-z^4 a^4+2 z^2 a^4+a^4+z^4 a^2+2 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{15}-4 z^5 a^{15}+4 z^3 a^{15}-z a^{15}+3 z^8 a^{14}-11 z^6 a^{14}+10 z^4 a^{14}-2 z^2 a^{14}+5 z^9 a^{13}-18 z^7 a^{13}+20 z^5 a^{13}-11 z^3 a^{13}+3 z a^{13}+5 z^{10} a^{12}-15 z^8 a^{12}+14 z^6 a^{12}-8 z^4 a^{12}+3 z^2 a^{12}-a^{12}+3 z^{11} a^{11}-3 z^9 a^{11}-9 z^7 a^{11}+15 z^5 a^{11}-7 z^3 a^{11}-z a^{11}+z^{12} a^{10}+5 z^{10} a^{10}-19 z^8 a^{10}+25 z^6 a^{10}-15 z^4 a^{10}+3 z^2 a^{10}+6 z^{11} a^9-16 z^9 a^9+28 z^7 a^9-33 z^5 a^9+25 z^3 a^9-7 z a^9+z^{12} a^8+5 z^{10} a^8-15 z^8 a^8+23 z^6 a^8-16 z^4 a^8+5 z^2 a^8+a^8+3 z^{11} a^7-2 z^9 a^7+z^7 a^7-z^5 a^7+3 z^3 a^7-2 z a^7+5 z^{10} a^6-9 z^8 a^6+10 z^6 a^6-7 z^4 a^6+z^2 a^6+6 z^9 a^5-14 z^7 a^5+15 z^5 a^5-9 z^3 a^5+5 z^8 a^4-12 z^6 a^4+9 z^4 a^4-4 z^2 a^4+a^4+3 z^7 a^3-8 z^5 a^3+5 z^3 a^3+z^6 a^2-3 z^4 a^2+2 z^2 a^2 }[/math] |
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