K13a825
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Polynomial invariants
| Jones polynomial | Data:K13a825/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-5 t^4+14 t^3-23 t^2+28 t-29+28 t^{-1} -23 t^{-2} +14 t^{-3} -5 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a825/Conway Polynomial |
| Determinant | 171 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-6} -z^8 a^{-4} +8 z^8 a^{-6} -2 z^8 a^{-8} -6 z^6 a^{-4} +26 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -12 z^4 a^{-4} +44 z^4 a^{-6} -25 z^4 a^{-8} +4 z^4 a^{-10} -10 z^2 a^{-4} +37 z^2 a^{-6} -24 z^2 a^{-8} +4 z^2 a^{-10} -3 a^{-4} +12 a^{-6} -10 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-6} +z^{12} a^{-8} +3 z^{11} a^{-5} +8 z^{11} a^{-7} +5 z^{11} a^{-9} +3 z^{10} a^{-4} +7 z^{10} a^{-6} +14 z^{10} a^{-8} +10 z^{10} a^{-10} +z^9 a^{-3} -12 z^9 a^{-5} -29 z^9 a^{-7} -4 z^9 a^{-9} +12 z^9 a^{-11} -18 z^8 a^{-4} -60 z^8 a^{-6} -81 z^8 a^{-8} -27 z^8 a^{-10} +12 z^8 a^{-12} -6 z^7 a^{-3} +3 z^7 a^{-5} +7 z^7 a^{-7} -38 z^7 a^{-9} -25 z^7 a^{-11} +11 z^7 a^{-13} +37 z^6 a^{-4} +127 z^6 a^{-6} +137 z^6 a^{-8} +22 z^6 a^{-10} -17 z^6 a^{-12} +8 z^6 a^{-14} +12 z^5 a^{-3} +31 z^5 a^{-5} +59 z^5 a^{-7} +68 z^5 a^{-9} +11 z^5 a^{-11} -13 z^5 a^{-13} +4 z^5 a^{-15} -34 z^4 a^{-4} -115 z^4 a^{-6} -106 z^4 a^{-8} -16 z^4 a^{-10} +z^4 a^{-12} -7 z^4 a^{-14} +z^4 a^{-16} -10 z^3 a^{-3} -36 z^3 a^{-5} -63 z^3 a^{-7} -43 z^3 a^{-9} -z^3 a^{-11} +3 z^3 a^{-13} -2 z^3 a^{-15} +15 z^2 a^{-4} +53 z^2 a^{-6} +46 z^2 a^{-8} +9 z^2 a^{-10} +2 z^2 a^{-12} +z^2 a^{-14} +3 z a^{-3} +11 z a^{-5} +20 z a^{-7} +12 z a^{-9} -3 a^{-4} -12 a^{-6} -10 a^{-8} -2 a^{-10} }[/math] |
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