K13a2344
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Polynomial invariants
| Jones polynomial | Data:K13a2344/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+13 t^3-38 t^2+66 t-77+66 t^{-1} -38 t^{-2} +13 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a2344/Conway Polynomial |
| Determinant | 315 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+2 a^4 z^6-3 a^2 z^6+z^6 a^{-2} -3 z^6-a^6 z^4+6 a^4 z^4-5 a^2 z^4+2 z^4 a^{-2} -2 z^4-2 a^6 z^2+7 a^4 z^2-8 a^2 z^2+2 z^2-a^6+4 a^4-5 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^2 z^{12}+3 z^{12}+9 a^3 z^{11}+18 a z^{11}+9 z^{11} a^{-1} +15 a^4 z^{10}+19 a^2 z^{10}+10 z^{10} a^{-2} +14 z^{10}+18 a^5 z^9+6 a^3 z^9-41 a z^9-24 z^9 a^{-1} +5 z^9 a^{-3} +15 a^6 z^8-11 a^4 z^8-57 a^2 z^8-38 z^8 a^{-2} +z^8 a^{-4} -70 z^8+9 a^7 z^7-27 a^5 z^7-51 a^3 z^7+12 a z^7+9 z^7 a^{-1} -18 z^7 a^{-3} +4 a^8 z^6-22 a^6 z^6-30 a^4 z^6+25 a^2 z^6+45 z^6 a^{-2} -3 z^6 a^{-4} +77 z^6+a^9 z^5-10 a^7 z^5+14 a^5 z^5+46 a^3 z^5+14 a z^5+11 z^5 a^{-1} +18 z^5 a^{-3} -4 a^8 z^4+17 a^6 z^4+46 a^4 z^4+20 a^2 z^4-16 z^4 a^{-2} +2 z^4 a^{-4} -23 z^4-a^9 z^3+5 a^7 z^3+a^5 z^3-16 a^3 z^3-13 a z^3-5 z^3 a^{-1} -3 z^3 a^{-3} +a^8 z^2-6 a^6 z^2-22 a^4 z^2-22 a^2 z^2-7 z^2-a^7 z-a^5 z+3 a^3 z+4 a z+z a^{-1} +a^6+4 a^4+5 a^2+3 }[/math] |
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