K13a1753
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Polynomial invariants
| Jones polynomial | Data:K13a1753/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+33 t^2-57 t+69-57 t^{-1} +33 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1753/Conway Polynomial |
| Determinant | 277 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-2 a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +3 z^6+a^4 z^4-6 a^2 z^4+6 z^4 a^{-2} -3 z^4 a^{-4} +3 z^4+2 a^4 z^2-6 a^2 z^2+3 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-2} +z^{12}+4 a z^{11}+8 z^{11} a^{-1} +4 z^{11} a^{-3} +8 a^2 z^{10}+15 z^{10} a^{-2} +7 z^{10} a^{-4} +16 z^{10}+10 a^3 z^9+14 a z^9+3 z^9 a^{-1} +6 z^9 a^{-3} +7 z^9 a^{-5} +8 a^4 z^8-36 z^8 a^{-2} -13 z^8 a^{-4} +4 z^8 a^{-6} -27 z^8+4 a^5 z^7-14 a^3 z^7-41 a z^7-39 z^7 a^{-1} -38 z^7 a^{-3} -21 z^7 a^{-5} +z^7 a^{-7} +a^6 z^6-15 a^4 z^6-24 a^2 z^6+24 z^6 a^{-2} -z^6 a^{-4} -13 z^6 a^{-6} +4 z^6-8 a^5 z^5+3 a^3 z^5+35 a z^5+47 z^5 a^{-1} +46 z^5 a^{-3} +20 z^5 a^{-5} -3 z^5 a^{-7} -2 a^6 z^4+10 a^4 z^4+27 a^2 z^4-2 z^4 a^{-2} +10 z^4 a^{-4} +12 z^4 a^{-6} +15 z^4+5 a^5 z^3+2 a^3 z^3-12 a z^3-21 z^3 a^{-1} -22 z^3 a^{-3} -8 z^3 a^{-5} +2 z^3 a^{-7} +a^6 z^2-4 a^4 z^2-13 a^2 z^2-2 z^2 a^{-2} -4 z^2 a^{-4} -3 z^2 a^{-6} -9 z^2-a^5 z-a^3 z+a z+3 z a^{-1} +3 z a^{-3} +z a^{-5} +a^4+2 a^2+2 }[/math] |
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