K13a917
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Polynomial invariants
| Jones polynomial | Data:K13a917/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-13 t^3+37 t^2-63 t+75-63 t^{-1} +37 t^{-2} -13 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a917/Conway Polynomial |
| Determinant | 305 |
| 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} +4 z^6-3 a^2 z^4-2 z^4 a^{-2} -5 z^4 a^{-4} +z^4 a^{-6} +8 z^4-3 a^2 z^2-6 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} +9 z^2-a^2-3 a^{-2} + a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +8 z^{11} a^{-1} +14 z^{11} a^{-3} +6 z^{11} a^{-5} +24 z^{10} a^{-2} +16 z^{10} a^{-4} +7 z^{10} a^{-6} +15 z^{10}+18 a z^9+12 z^9 a^{-1} -18 z^9 a^{-3} -8 z^9 a^{-5} +4 z^9 a^{-7} +15 a^2 z^8-67 z^8 a^{-2} -65 z^8 a^{-4} -24 z^8 a^{-6} +z^8 a^{-8} -12 z^8+9 a^3 z^7-27 a z^7-66 z^7 a^{-1} -38 z^7 a^{-3} -24 z^7 a^{-5} -16 z^7 a^{-7} +4 a^4 z^6-22 a^2 z^6+37 z^6 a^{-2} +66 z^6 a^{-4} +25 z^6 a^{-6} -4 z^6 a^{-8} -26 z^6+a^5 z^5-10 a^3 z^5+14 a z^5+64 z^5 a^{-1} +65 z^5 a^{-3} +48 z^5 a^{-5} +22 z^5 a^{-7} -4 a^4 z^4+17 a^2 z^4+9 z^4 a^{-2} -24 z^4 a^{-4} -8 z^4 a^{-6} +5 z^4 a^{-8} +41 z^4-a^5 z^3+5 a^3 z^3+a z^3-24 z^3 a^{-1} -35 z^3 a^{-3} -28 z^3 a^{-5} -12 z^3 a^{-7} +a^4 z^2-6 a^2 z^2-14 z^2 a^{-2} +2 z^2 a^{-4} +z^2 a^{-6} -2 z^2 a^{-8} -20 z^2-a^3 z-a z+3 z a^{-1} +7 z a^{-3} +6 z a^{-5} +2 z a^{-7} +a^2+3 a^{-2} + a^{-4} +4 }[/math] |
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