K13a69
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Polynomial invariants
| Jones polynomial | Data:K13a69/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-36 t^2+80 t-103+80 t^{-1} -36 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | Data:K13a69/Conway Polynomial |
| Determinant | 355 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+4 z^2 a^8+4 a^8-6 z^4 a^6-12 z^2 a^6-8 a^6+4 z^6 a^4+12 z^4 a^4+17 z^2 a^4+9 a^4-z^8 a^2-4 z^6 a^2-10 z^4 a^2-11 z^2 a^2-5 a^2+z^6+2 z^4+3 z^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^6 z^{12}+a^4 z^{12}+4 a^7 z^{11}+10 a^5 z^{11}+6 a^3 z^{11}+7 a^8 z^{10}+23 a^6 z^{10}+31 a^4 z^{10}+15 a^2 z^{10}+7 a^9 z^9+19 a^7 z^9+29 a^5 z^9+36 a^3 z^9+19 a z^9+4 a^{10} z^8-2 a^8 z^8-33 a^6 z^8-41 a^4 z^8-a^2 z^8+13 z^8+a^{11} z^7-16 a^9 z^7-68 a^7 z^7-123 a^5 z^7-109 a^3 z^7-32 a z^7+5 z^7 a^{-1} -12 a^{10} z^6-30 a^8 z^6-31 a^6 z^6-40 a^4 z^6-50 a^2 z^6+z^6 a^{-2} -22 z^6-3 a^{11} z^5+11 a^9 z^5+72 a^7 z^5+134 a^5 z^5+103 a^3 z^5+21 a z^5-6 z^5 a^{-1} +13 a^{10} z^4+44 a^8 z^4+77 a^6 z^4+88 a^4 z^4+59 a^2 z^4-z^4 a^{-2} +16 z^4+3 a^{11} z^3-2 a^9 z^3-32 a^7 z^3-60 a^5 z^3-46 a^3 z^3-11 a z^3+2 z^3 a^{-1} -6 a^{10} z^2-23 a^8 z^2-44 a^6 z^2-48 a^4 z^2-29 a^2 z^2-8 z^2-a^{11} z+5 a^7 z+10 a^5 z+9 a^3 z+3 a z+a^{10}+4 a^8+8 a^6+9 a^4+5 a^2+2 }[/math] |
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