K13a3111
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Polynomial invariants
| Jones polynomial | Data:K13a3111/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 4 t^4-12 t^3+21 t^2-28 t+31-28 t^{-1} +21 t^{-2} -12 t^{-3} +4 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3111/Conway Polynomial |
| Determinant | 161 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +2 z^8 a^{-10} +z^8 a^{-12} +6 z^6 a^{-8} +11 z^6 a^{-10} +4 z^6 a^{-12} -z^6 a^{-14} +12 z^4 a^{-8} +19 z^4 a^{-10} +2 z^4 a^{-12} -4 z^4 a^{-14} +9 z^2 a^{-8} +12 z^2 a^{-10} -6 z^2 a^{-12} -3 z^2 a^{-14} +2 a^{-8} +3 a^{-10} -5 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-12} +z^{12} a^{-14} +2 z^{11} a^{-11} +5 z^{11} a^{-13} +3 z^{11} a^{-15} +3 z^{10} a^{-10} +z^{10} a^{-12} +3 z^{10} a^{-14} +5 z^{10} a^{-16} +2 z^9 a^{-9} -3 z^9 a^{-11} -15 z^9 a^{-13} -4 z^9 a^{-15} +6 z^9 a^{-17} +z^8 a^{-8} -13 z^8 a^{-10} -10 z^8 a^{-12} -12 z^8 a^{-14} -10 z^8 a^{-16} +6 z^8 a^{-18} -9 z^7 a^{-9} -11 z^7 a^{-11} +16 z^7 a^{-13} +2 z^7 a^{-15} -11 z^7 a^{-17} +5 z^7 a^{-19} -6 z^6 a^{-8} +19 z^6 a^{-10} +13 z^6 a^{-12} +13 z^6 a^{-14} +11 z^6 a^{-16} -11 z^6 a^{-18} +3 z^6 a^{-20} +11 z^5 a^{-9} +24 z^5 a^{-11} -7 z^5 a^{-13} -z^5 a^{-15} +8 z^5 a^{-17} -10 z^5 a^{-19} +z^5 a^{-21} +12 z^4 a^{-8} -16 z^4 a^{-10} -20 z^4 a^{-12} -10 z^4 a^{-14} -4 z^4 a^{-16} +8 z^4 a^{-18} -6 z^4 a^{-20} -2 z^3 a^{-9} -19 z^3 a^{-11} -11 z^3 a^{-13} +z^3 a^{-15} +4 z^3 a^{-17} +7 z^3 a^{-19} -2 z^3 a^{-21} -9 z^2 a^{-8} +11 z^2 a^{-10} +18 z^2 a^{-12} +2 z^2 a^{-14} +2 z^2 a^{-16} +2 z^2 a^{-20} -z a^{-9} +7 z a^{-11} +7 z a^{-13} -z a^{-15} -2 z a^{-17} -2 z a^{-19} +2 a^{-8} -3 a^{-10} -5 a^{-12} - a^{-14} }[/math] |
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