K12a52
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{16}-3 q^{15}+6 q^{14}-10 q^{13}+13 q^{12}-16 q^{11}+16 q^{10}-15 q^9+12 q^8-8 q^7+6 q^6-2 q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^4-9 t^3+15 t^2-18 t+19-18 t^{-1} +15 t^{-2} -9 t^{-3} +3 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^8+15 z^6+21 z^4+9 z^2+1 }[/math] |
| Determinant | 109 |
| Signature | 8 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +2 z^8 a^{-10} +6 z^6 a^{-8} +12 z^6 a^{-10} -3 z^6 a^{-12} +12 z^4 a^{-8} +23 z^4 a^{-10} -15 z^4 a^{-12} +z^4 a^{-14} +10 z^2 a^{-8} +16 z^2 a^{-10} -21 z^2 a^{-12} +4 z^2 a^{-14} +3 a^{-8} +3 a^{-10} -8 a^{-12} +3 a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-11} +z^{11} a^{-13} +3 z^{10} a^{-10} +7 z^{10} a^{-12} +4 z^{10} a^{-14} +2 z^9 a^{-9} +4 z^9 a^{-11} +8 z^9 a^{-13} +6 z^9 a^{-15} +z^8 a^{-8} -14 z^8 a^{-10} -29 z^8 a^{-12} -8 z^8 a^{-14} +6 z^8 a^{-16} -9 z^7 a^{-9} -36 z^7 a^{-11} -47 z^7 a^{-13} -14 z^7 a^{-15} +6 z^7 a^{-17} -6 z^6 a^{-8} +21 z^6 a^{-10} +40 z^6 a^{-12} +z^6 a^{-14} -7 z^6 a^{-16} +5 z^6 a^{-18} +10 z^5 a^{-9} +64 z^5 a^{-11} +79 z^5 a^{-13} +16 z^5 a^{-15} -6 z^5 a^{-17} +3 z^5 a^{-19} +12 z^4 a^{-8} -18 z^4 a^{-10} -35 z^4 a^{-12} +z^4 a^{-14} -5 z^4 a^{-18} +z^4 a^{-20} -z^3 a^{-9} -43 z^3 a^{-11} -61 z^3 a^{-13} -15 z^3 a^{-15} +z^3 a^{-17} -3 z^3 a^{-19} -10 z^2 a^{-8} +12 z^2 a^{-10} +26 z^2 a^{-12} +2 z^2 a^{-14} +z^2 a^{-16} +2 z^2 a^{-18} -z^2 a^{-20} -2 z a^{-9} +11 z a^{-11} +18 z a^{-13} +5 z a^{-15} +z a^{-17} +z a^{-19} +3 a^{-8} -3 a^{-10} -8 a^{-12} -3 a^{-14} }[/math] |
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