K13a4037
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Polynomial invariants
| Jones polynomial | Data:K13a4037/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-14 t^3+46 t^2-89 t+111-89 t^{-1} +46 t^{-2} -14 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a4037/Conway Polynomial |
| Determinant | 413 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+2 z^6 a^{-2} -2 z^6 a^{-4} +3 z^6-2 a^2 z^4+2 z^4 a^{-2} -4 z^4 a^{-4} +z^4 a^{-6} +5 z^4-2 a^2 z^2+2 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} +3 z^2+2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{12} a^{-2} +5 z^{12} a^{-4} +19 z^{11} a^{-1} +31 z^{11} a^{-3} +12 z^{11} a^{-5} +42 z^{10} a^{-2} +20 z^{10} a^{-4} +11 z^{10} a^{-6} +33 z^{10}+36 a z^9-2 z^9 a^{-1} -72 z^9 a^{-3} -29 z^9 a^{-5} +5 z^9 a^{-7} +27 a^2 z^8-149 z^8 a^{-2} -109 z^8 a^{-4} -38 z^8 a^{-6} +z^8 a^{-8} -52 z^8+14 a^3 z^7-61 a z^7-79 z^7 a^{-1} +17 z^7 a^{-3} +4 z^7 a^{-5} -17 z^7 a^{-7} +5 a^4 z^6-36 a^2 z^6+145 z^6 a^{-2} +140 z^6 a^{-4} +44 z^6 a^{-6} -3 z^6 a^{-8} +11 z^6+a^5 z^5-10 a^3 z^5+36 a z^5+81 z^5 a^{-1} +44 z^5 a^{-3} +28 z^5 a^{-5} +18 z^5 a^{-7} -a^4 z^4+19 a^2 z^4-59 z^4 a^{-2} -69 z^4 a^{-4} -22 z^4 a^{-6} +2 z^4 a^{-8} +6 z^4+3 a^3 z^3-11 a z^3-29 z^3 a^{-1} -25 z^3 a^{-3} -17 z^3 a^{-5} -7 z^3 a^{-7} -4 a^2 z^2+13 z^2 a^{-2} +15 z^2 a^{-4} +4 z^2 a^{-6} -2 z^2+a z+3 z a^{-1} +4 z a^{-3} +2 z a^{-5} -2 a^{-2} - a^{-4} }[/math] |
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