K13a2457
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Polynomial invariants
| Jones polynomial | Data:K13a2457/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^5+6 t^4-18 t^3+36 t^2-51 t+57-51 t^{-1} +36 t^{-2} -18 t^{-3} +6 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | Data:K13a2457/Conway Polynomial |
| Determinant | 281 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -7 z^8 a^{-4} +2 z^8 a^{-6} +5 z^6 a^{-2} -20 z^6 a^{-4} +11 z^6 a^{-6} -z^6 a^{-8} +9 z^4 a^{-2} -29 z^4 a^{-4} +22 z^4 a^{-6} -4 z^4 a^{-8} +8 z^2 a^{-2} -20 z^2 a^{-4} +19 z^2 a^{-6} -5 z^2 a^{-8} +3 a^{-2} -5 a^{-4} +5 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-4} +2 z^{12} a^{-6} +6 z^{11} a^{-3} +14 z^{11} a^{-5} +8 z^{11} a^{-7} +7 z^{10} a^{-2} +14 z^{10} a^{-4} +22 z^{10} a^{-6} +15 z^{10} a^{-8} +4 z^9 a^{-1} -12 z^9 a^{-3} -30 z^9 a^{-5} +3 z^9 a^{-7} +17 z^9 a^{-9} -26 z^8 a^{-2} -70 z^8 a^{-4} -84 z^8 a^{-6} -27 z^8 a^{-8} +14 z^8 a^{-10} +z^8-16 z^7 a^{-1} -12 z^7 a^{-3} -7 z^7 a^{-5} -51 z^7 a^{-7} -31 z^7 a^{-9} +9 z^7 a^{-11} +30 z^6 a^{-2} +97 z^6 a^{-4} +109 z^6 a^{-6} +22 z^6 a^{-8} -20 z^6 a^{-10} +4 z^6 a^{-12} -4 z^6+20 z^5 a^{-1} +31 z^5 a^{-3} +46 z^5 a^{-5} +75 z^5 a^{-7} +28 z^5 a^{-9} -11 z^5 a^{-11} +z^5 a^{-13} -16 z^4 a^{-2} -68 z^4 a^{-4} -78 z^4 a^{-6} -16 z^4 a^{-8} +11 z^4 a^{-10} -4 z^4 a^{-12} +5 z^4-9 z^3 a^{-1} -16 z^3 a^{-3} -34 z^3 a^{-5} -49 z^3 a^{-7} -16 z^3 a^{-9} +5 z^3 a^{-11} -z^3 a^{-13} +8 z^2 a^{-2} +30 z^2 a^{-4} +30 z^2 a^{-6} +8 z^2 a^{-8} -z^2 a^{-10} +z^2 a^{-12} -2 z^2+z a^{-1} +4 z a^{-3} +8 z a^{-5} +10 z a^{-7} +5 z a^{-9} -3 a^{-2} -5 a^{-4} -5 a^{-6} -2 a^{-8} }[/math] |
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