K12n688
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{16}-3 q^{15}+5 q^{14}-7 q^{13}+7 q^{12}-7 q^{11}+5 q^{10}-3 q^9+q^8+q^7+q^5 }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-t^4-t^3+5 t^2-9 t+11-9 t^{-1} +5 t^{-2} - t^{-3} - t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+9 z^8+26 z^6+29 z^4+11 z^2+1 }[/math] |
| Determinant | 37 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-10} +10 z^8 a^{-10} -z^8 a^{-12} +36 z^6 a^{-10} -10 z^6 a^{-12} +58 z^4 a^{-10} -31 z^4 a^{-12} +2 z^4 a^{-14} +41 z^2 a^{-10} -36 z^2 a^{-12} +6 z^2 a^{-14} +10 a^{-10} -13 a^{-12} +4 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-11} +z^9 a^{-13} -10 z^8 a^{-10} -11 z^8 a^{-12} +z^8 a^{-16} -10 z^7 a^{-11} -10 z^7 a^{-13} +3 z^7 a^{-15} +3 z^7 a^{-17} +36 z^6 a^{-10} +41 z^6 a^{-12} +4 z^6 a^{-14} +3 z^6 a^{-16} +4 z^6 a^{-18} +31 z^5 a^{-11} +34 z^5 a^{-13} -2 z^5 a^{-15} -2 z^5 a^{-17} +3 z^5 a^{-19} -58 z^4 a^{-10} -66 z^4 a^{-12} -7 z^4 a^{-14} -5 z^4 a^{-16} -5 z^4 a^{-18} +z^4 a^{-20} -36 z^3 a^{-11} -40 z^3 a^{-13} -z^3 a^{-15} -z^3 a^{-17} -4 z^3 a^{-19} +41 z^2 a^{-10} +48 z^2 a^{-12} +7 z^2 a^{-14} +2 z^2 a^{-16} +z^2 a^{-18} -z^2 a^{-20} +13 z a^{-11} +14 z a^{-13} +z a^{-15} +z a^{-17} +z a^{-19} -10 a^{-10} -13 a^{-12} -4 a^{-14} }[/math] |
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