K13a4159
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Polynomial invariants
| Jones polynomial | Data:K13a4159/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -3 t^4+17 t^3-45 t^2+78 t-93+78 t^{-1} -45 t^{-2} +17 t^{-3} -3 t^{-4} }[/math] |
| Conway polynomial | Data:K13a4159/Conway Polynomial |
| Determinant | 379 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-2 a^8+3 z^6 a^6+11 z^4 a^6+13 z^2 a^6+4 a^6-2 z^8 a^4-9 z^6 a^4-16 z^4 a^4-12 z^2 a^4-3 a^4-z^8 a^2-2 z^6 a^2+z^4 a^2+4 z^2 a^2+2 a^2+z^6+2 z^4+z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^6 z^{12}+4 a^4 z^{12}+10 a^7 z^{11}+24 a^5 z^{11}+14 a^3 z^{11}+11 a^8 z^{10}+17 a^6 z^{10}+28 a^4 z^{10}+22 a^2 z^{10}+8 a^9 z^9-15 a^7 z^9-53 a^5 z^9-9 a^3 z^9+21 a z^9+4 a^{10} z^8-24 a^8 z^8-67 a^6 z^8-93 a^4 z^8-41 a^2 z^8+13 z^8+a^{11} z^7-19 a^9 z^7+3 a^7 z^7+47 a^5 z^7-21 a^3 z^7-40 a z^7+5 z^7 a^{-1} -11 a^{10} z^6+18 a^8 z^6+95 a^6 z^6+119 a^4 z^6+31 a^2 z^6+z^6 a^{-2} -21 z^6-3 a^{11} z^5+12 a^9 z^5+4 a^7 z^5-18 a^5 z^5+26 a^3 z^5+27 a z^5-6 z^5 a^{-1} +9 a^{10} z^4-12 a^8 z^4-74 a^6 z^4-82 a^4 z^4-18 a^2 z^4-z^4 a^{-2} +10 z^4+3 a^{11} z^3-2 a^9 z^3-6 a^7 z^3-a^5 z^3-10 a^3 z^3-9 a z^3+z^3 a^{-1} -2 a^{10} z^2+8 a^8 z^2+28 a^6 z^2+29 a^4 z^2+9 a^2 z^2-2 z^2-a^{11} z+a^9 z+2 a^7 z+a^5 z+2 a^3 z+a z-2 a^8-4 a^6-3 a^4-2 a^2 }[/math] |
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