K13a3135
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Polynomial invariants
| Jones polynomial | Data:K13a3135/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 3 t^4-9 t^3+16 t^2-21 t+23-21 t^{-1} +16 t^{-2} -9 t^{-3} +3 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3135/Conway Polynomial |
| Determinant | 121 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +z^8 a^{-12} +7 z^6 a^{-8} +4 z^6 a^{-10} +5 z^6 a^{-12} -z^6 a^{-14} +17 z^4 a^{-8} +z^4 a^{-10} +8 z^4 a^{-12} -4 z^4 a^{-14} +17 z^2 a^{-8} -9 z^2 a^{-10} +6 z^2 a^{-12} -4 z^2 a^{-14} +6 a^{-8} -7 a^{-10} +3 a^{-12} - a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-12} +z^{12} a^{-14} +z^{11} a^{-11} +4 z^{11} a^{-13} +3 z^{11} a^{-15} +z^{10} a^{-10} -5 z^{10} a^{-12} -z^{10} a^{-14} +5 z^{10} a^{-16} +z^9 a^{-9} -3 z^9 a^{-11} -21 z^9 a^{-13} -11 z^9 a^{-15} +6 z^9 a^{-17} +z^8 a^{-8} -2 z^8 a^{-10} +16 z^8 a^{-12} -5 z^8 a^{-14} -18 z^8 a^{-16} +6 z^8 a^{-18} -4 z^7 a^{-9} +4 z^7 a^{-11} +50 z^7 a^{-13} +19 z^7 a^{-15} -18 z^7 a^{-17} +5 z^7 a^{-19} -7 z^6 a^{-8} -8 z^6 a^{-10} -32 z^6 a^{-12} +16 z^6 a^{-14} +29 z^6 a^{-16} -15 z^6 a^{-18} +3 z^6 a^{-20} +z^5 a^{-9} -14 z^5 a^{-11} -61 z^5 a^{-13} -11 z^5 a^{-15} +23 z^5 a^{-17} -11 z^5 a^{-19} +z^5 a^{-21} +17 z^4 a^{-8} +23 z^4 a^{-10} +25 z^4 a^{-12} -15 z^4 a^{-14} -14 z^4 a^{-16} +14 z^4 a^{-18} -6 z^4 a^{-20} +9 z^3 a^{-9} +21 z^3 a^{-11} +28 z^3 a^{-13} +z^3 a^{-15} -7 z^3 a^{-17} +6 z^3 a^{-19} -2 z^3 a^{-21} -17 z^2 a^{-8} -20 z^2 a^{-10} -9 z^2 a^{-12} +2 z^2 a^{-16} -3 z^2 a^{-18} +z^2 a^{-20} -7 z a^{-9} -9 z a^{-11} -4 z a^{-13} +z a^{-17} -z a^{-19} +6 a^{-8} +7 a^{-10} +3 a^{-12} + a^{-14} }[/math] |
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