K12a763
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-2 q^{11}+4 q^{10}-8 q^9+11 q^8-14 q^7+15 q^6-14 q^5+12 q^4-8 q^3+5 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+14 t^2-20 t+21-20 t^{-1} +14 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-10 z^4+1 }[/math] |
| Determinant | 97 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -2 z^4 a^{-4} -7 z^4 a^{-6} -3 z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} +2 z^2 a^{-4} -6 z^2 a^{-6} -2 z^2 a^{-8} +3 z^2 a^{-10} + a^{-2} +2 a^{-4} -2 a^{-6} - a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +4 z^{10} a^{-8} +2 z^{10} a^{-10} +3 z^9 a^{-5} -z^9 a^{-7} -2 z^9 a^{-9} +2 z^9 a^{-11} +3 z^8 a^{-4} -3 z^8 a^{-6} -15 z^8 a^{-8} -7 z^8 a^{-10} +2 z^8 a^{-12} +2 z^7 a^{-3} -8 z^7 a^{-5} +z^7 a^{-7} +5 z^7 a^{-9} -4 z^7 a^{-11} +2 z^7 a^{-13} +z^6 a^{-2} -9 z^6 a^{-4} -4 z^6 a^{-6} +29 z^6 a^{-8} +18 z^6 a^{-10} -4 z^6 a^{-12} +z^6 a^{-14} -6 z^5 a^{-3} +6 z^5 a^{-5} -2 z^5 a^{-7} -3 z^5 a^{-9} +4 z^5 a^{-11} -7 z^5 a^{-13} -4 z^4 a^{-2} +8 z^4 a^{-4} +15 z^4 a^{-6} -22 z^4 a^{-8} -21 z^4 a^{-10} -4 z^4 a^{-14} +3 z^3 a^{-3} +8 z^3 a^{-7} -4 z^3 a^{-11} +7 z^3 a^{-13} +4 z^2 a^{-2} -6 z^2 a^{-4} -11 z^2 a^{-6} +9 z^2 a^{-8} +7 z^2 a^{-10} +z^2 a^{-12} +4 z^2 a^{-14} -3 z a^{-5} -3 z a^{-7} +z a^{-9} -z a^{-11} -2 z a^{-13} - a^{-2} +2 a^{-4} +2 a^{-6} - a^{-8} - a^{-10} }[/math] |
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