K13a4531
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Polynomial invariants
| Jones polynomial | Data:K13a4531/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-20 t^2+47 t-61+47 t^{-1} -20 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | Data:K13a4531/Conway Polynomial |
| Determinant | 203 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^{10}+a^{10}-2 z^4 a^8-4 z^2 a^8-3 a^8+z^6 a^6+z^4 a^6+z^2 a^6+a^6+2 z^6 a^4+5 z^4 a^4+6 z^2 a^4+2 a^4+z^6 a^2+z^4 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^8 a^{12}-5 z^6 a^{12}+7 z^4 a^{12}-2 z^2 a^{12}+3 z^9 a^{11}-15 z^7 a^{11}+24 z^5 a^{11}-14 z^3 a^{11}+2 z a^{11}+4 z^{10} a^{10}-17 z^8 a^{10}+22 z^6 a^{10}-11 z^4 a^{10}+3 z^2 a^{10}-a^{10}+3 z^{11} a^9-7 z^9 a^9-5 z^7 a^9+19 z^5 a^9-16 z^3 a^9+5 z a^9+z^{12} a^8+6 z^{10} a^8-33 z^8 a^8+50 z^6 a^8-40 z^4 a^8+17 z^2 a^8-3 a^8+7 z^{11} a^7-19 z^9 a^7+16 z^7 a^7-9 z^5 a^7+2 z^3 a^7+z a^7+z^{12} a^6+10 z^{10} a^6-36 z^8 a^6+43 z^6 a^6-26 z^4 a^6+8 z^2 a^6-a^6+4 z^{11} a^5+2 z^9 a^5-21 z^7 a^5+22 z^5 a^5-4 z^3 a^5-2 z a^5+8 z^{10} a^4-10 z^8 a^4-2 z^6 a^4+12 z^4 a^4-8 z^2 a^4+2 a^4+11 z^9 a^3-19 z^7 a^3+14 z^5 a^3-4 z^3 a^3+11 z^8 a^2-18 z^6 a^2+11 z^4 a^2-3 z^2 a^2+8 z^7 a-11 z^5 a+3 z^3 a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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