K13a2083
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Polynomial invariants
| Jones polynomial | Data:K13a2083/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -3 t^4+13 t^3-27 t^2+36 t-37+36 t^{-1} -27 t^{-2} +13 t^{-3} -3 t^{-4} }[/math] |
| Conway polynomial | Data:K13a2083/Conway Polynomial |
| Determinant | 195 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-2 z^8+a^4 z^6-4 a^2 z^6+3 z^6 a^{-2} -11 z^6+4 a^4 z^4-4 a^2 z^4+13 z^4 a^{-2} -z^4 a^{-4} -21 z^4+4 a^4 z^2-a^2 z^2+15 z^2 a^{-2} -3 z^2 a^{-4} -18 z^2+a^4+a^2+5 a^{-2} - a^{-4} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12}+7 a z^{11}+12 z^{11} a^{-1} +5 z^{11} a^{-3} +11 a^2 z^{10}+4 z^{10} a^{-2} +4 z^{10} a^{-4} +11 z^{10}+13 a^3 z^9-13 a z^9-50 z^9 a^{-1} -23 z^9 a^{-3} +z^9 a^{-5} +13 a^4 z^8-25 a^2 z^8-58 z^8 a^{-2} -22 z^8 a^{-4} -74 z^8+10 a^5 z^7-27 a^3 z^7-12 a z^7+57 z^7 a^{-1} +27 z^7 a^{-3} -5 z^7 a^{-5} +6 a^6 z^6-26 a^4 z^6+7 a^2 z^6+122 z^6 a^{-2} +40 z^6 a^{-4} +121 z^6+3 a^7 z^5-15 a^5 z^5+10 a^3 z^5+20 a z^5-14 z^5 a^{-1} +2 z^5 a^{-3} +8 z^5 a^{-5} +a^8 z^4-5 a^6 z^4+20 a^4 z^4+3 a^2 z^4-96 z^4 a^{-2} -28 z^4 a^{-4} -91 z^4-2 a^7 z^3+11 a^5 z^3+3 a^3 z^3-7 a z^3-4 z^3 a^{-1} -12 z^3 a^{-3} -5 z^3 a^{-5} -a^8 z^2+2 a^6 z^2-7 a^4 z^2-2 a^2 z^2+34 z^2 a^{-2} +7 z^2 a^{-4} +35 z^2-2 a^5 z-2 a^3 z+2 z a^{-1} +3 z a^{-3} +z a^{-5} +a^4-a^2-5 a^{-2} - a^{-4} -5 }[/math] |
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