K13a3712
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Polynomial invariants
| Jones polynomial | Data:K13a3712/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 5 t^4-16 t^3+28 t^2-35 t+37-35 t^{-1} +28 t^{-2} -16 t^{-3} +5 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3712/Conway Polynomial |
| Determinant | 205 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +3 z^8 a^{-10} +z^8 a^{-12} +5 z^6 a^{-8} +18 z^6 a^{-10} +2 z^6 a^{-12} -z^6 a^{-14} +7 z^4 a^{-8} +36 z^4 a^{-10} -8 z^4 a^{-12} -3 z^4 a^{-14} +3 z^2 a^{-8} +29 z^2 a^{-10} -19 z^2 a^{-12} +8 a^{-10} -9 a^{-12} +2 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-12} +2 z^{12} a^{-14} +5 z^{11} a^{-11} +11 z^{11} a^{-13} +6 z^{11} a^{-15} +6 z^{10} a^{-10} +4 z^{10} a^{-12} +7 z^{10} a^{-14} +9 z^{10} a^{-16} +3 z^9 a^{-9} -17 z^9 a^{-11} -41 z^9 a^{-13} -11 z^9 a^{-15} +10 z^9 a^{-17} +z^8 a^{-8} -30 z^8 a^{-10} -47 z^8 a^{-12} -45 z^8 a^{-14} -19 z^8 a^{-16} +10 z^8 a^{-18} -13 z^7 a^{-9} +5 z^7 a^{-11} +42 z^7 a^{-13} +z^7 a^{-15} -15 z^7 a^{-17} +8 z^7 a^{-19} -5 z^6 a^{-8} +53 z^6 a^{-10} +90 z^6 a^{-12} +69 z^6 a^{-14} +19 z^6 a^{-16} -14 z^6 a^{-18} +4 z^6 a^{-20} +14 z^5 a^{-9} +24 z^5 a^{-11} +2 z^5 a^{-13} +11 z^5 a^{-15} +6 z^5 a^{-17} -12 z^5 a^{-19} +z^5 a^{-21} +7 z^4 a^{-8} -54 z^4 a^{-10} -79 z^4 a^{-12} -39 z^4 a^{-14} -12 z^4 a^{-16} +4 z^4 a^{-18} -5 z^4 a^{-20} -4 z^3 a^{-9} -27 z^3 a^{-11} -23 z^3 a^{-13} -7 z^3 a^{-15} -z^3 a^{-17} +5 z^3 a^{-19} -z^3 a^{-21} -3 z^2 a^{-8} +33 z^2 a^{-10} +39 z^2 a^{-12} +8 z^2 a^{-14} +4 z^2 a^{-16} +z^2 a^{-20} +9 z a^{-11} +8 z a^{-13} +z a^{-15} +z a^{-17} -z a^{-19} -8 a^{-10} -9 a^{-12} -2 a^{-14} }[/math] |
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