K12a741
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+11 q^{10}-20 q^9+28 q^8-36 q^7+38 q^6-35 q^5+29 q^4-19 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+25 t^2-54 t+69-54 t^{-1} +25 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-5 z^4+z^2+1 }[/math] |
| Determinant | 237 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -8 z^4 a^{-6} +z^4 a^{-10} +z^2 a^{-2} +6 z^2 a^{-4} -8 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} +4 a^{-4} -3 a^{-6} - a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +7 z^{10} a^{-6} +14 z^{10} a^{-8} +7 z^{10} a^{-10} +11 z^9 a^{-5} +22 z^9 a^{-7} +22 z^9 a^{-9} +11 z^9 a^{-11} +9 z^8 a^{-4} +7 z^8 a^{-6} -4 z^8 a^{-8} +7 z^8 a^{-10} +9 z^8 a^{-12} +4 z^7 a^{-3} -18 z^7 a^{-5} -48 z^7 a^{-7} -47 z^7 a^{-9} -17 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -19 z^6 a^{-4} -42 z^6 a^{-6} -41 z^6 a^{-8} -38 z^6 a^{-10} -18 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +9 z^5 a^{-5} +26 z^5 a^{-7} +25 z^5 a^{-9} +8 z^5 a^{-11} -7 z^5 a^{-13} -2 z^4 a^{-2} +18 z^4 a^{-4} +47 z^4 a^{-6} +44 z^4 a^{-8} +34 z^4 a^{-10} +15 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} -5 z^3 a^{-9} -4 z^3 a^{-11} +4 z^3 a^{-13} +z^2 a^{-2} -12 z^2 a^{-4} -22 z^2 a^{-6} -11 z^2 a^{-8} -10 z^2 a^{-10} -7 z^2 a^{-12} +z^2 a^{-14} -3 z a^{-5} -z a^{-7} +5 z a^{-9} +2 z a^{-11} -z a^{-13} +4 a^{-4} +3 a^{-6} - a^{-8} - a^{-10} }[/math] |
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