K13a1009
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Polynomial invariants
| Jones polynomial | Data:K13a1009/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^4+10 t^3-43 t^2+96 t-123+96 t^{-1} -43 t^{-2} +10 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | Data:K13a1009/Conway Polynomial |
| Determinant | 423 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-3 z^4 a^6-2 z^2 a^6+3 z^6 a^4+5 z^4 a^4+4 z^2 a^4+2 a^4-z^8 a^2-3 z^6 a^2-8 z^4 a^2-9 z^2 a^2-4 a^2+2 z^6+4 z^4+5 z^2+3-z^4 a^{-2} -z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{12}+3 a^2 z^{12}+12 a^5 z^{11}+22 a^3 z^{11}+10 a z^{11}+21 a^6 z^{10}+40 a^4 z^{10}+33 a^2 z^{10}+14 z^{10}+21 a^7 z^9+19 a^5 z^9-6 a^3 z^9+7 a z^9+11 z^9 a^{-1} +13 a^8 z^8-22 a^6 z^8-87 a^4 z^8-79 a^2 z^8+5 z^8 a^{-2} -22 z^8+5 a^9 z^7-35 a^7 z^7-82 a^5 z^7-76 a^3 z^7-60 a z^7-25 z^7 a^{-1} +z^7 a^{-3} +a^{10} z^6-20 a^8 z^6-9 a^6 z^6+41 a^4 z^6+37 a^2 z^6-12 z^6 a^{-2} -4 z^6-6 a^9 z^5+25 a^7 z^5+74 a^5 z^5+85 a^3 z^5+63 a z^5+19 z^5 a^{-1} -2 z^5 a^{-3} -a^{10} z^4+13 a^8 z^4+18 a^6 z^4+11 a^4 z^4+20 a^2 z^4+10 z^4 a^{-2} +23 z^4+2 a^9 z^3-10 a^7 z^3-24 a^5 z^3-30 a^3 z^3-25 a z^3-6 z^3 a^{-1} +z^3 a^{-3} -4 a^8 z^2-6 a^6 z^2-11 a^4 z^2-21 a^2 z^2-3 z^2 a^{-2} -15 z^2+a^7 z+2 a^5 z+4 a^3 z+4 a z+z a^{-1} +2 a^4+4 a^2+3 }[/math] |
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