K12a539
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+6 q^{10}-12 q^9+17 q^8-21 q^7+23 q^6-21 q^5+18 q^4-12 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+18 t^2-32 t+37-32 t^{-1} +18 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-6 z^4+4 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -5 z^4 a^{-6} -2 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} +2 z^2 a^{-10} +2 a^{-4} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^{10} a^{-10} +5 z^9 a^{-5} +6 z^9 a^{-7} +5 z^9 a^{-9} +4 z^9 a^{-11} +5 z^8 a^{-4} -12 z^8 a^{-8} -3 z^8 a^{-10} +4 z^8 a^{-12} +3 z^7 a^{-3} -10 z^7 a^{-5} -15 z^7 a^{-7} -10 z^7 a^{-9} -5 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -13 z^6 a^{-4} -8 z^6 a^{-6} +21 z^6 a^{-8} +6 z^6 a^{-10} -8 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +8 z^5 a^{-5} +20 z^5 a^{-7} +10 z^5 a^{-9} -3 z^5 a^{-11} -9 z^5 a^{-13} -3 z^4 a^{-2} +12 z^4 a^{-4} +9 z^4 a^{-6} -23 z^4 a^{-8} -12 z^4 a^{-10} +2 z^4 a^{-12} -3 z^4 a^{-14} +5 z^3 a^{-3} -5 z^3 a^{-5} -16 z^3 a^{-7} -6 z^3 a^{-9} +8 z^3 a^{-11} +8 z^3 a^{-13} +2 z^2 a^{-2} -7 z^2 a^{-4} -4 z^2 a^{-6} +11 z^2 a^{-8} +6 z^2 a^{-10} +2 z^2 a^{-12} +2 z^2 a^{-14} +z a^{-5} +5 z a^{-7} +z a^{-9} -5 z a^{-11} -2 z a^{-13} +2 a^{-4} - a^{-8} }[/math] |
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