K12a238
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-14 q^9+19 q^8-23 q^7+23 q^6-21 q^5+16 q^4-10 q^3+6 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+17 t^2-33 t+41-33 t^{-1} +17 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-7 z^4-z^2+1 }[/math] |
| Determinant | 149 |
| 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} -6 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} -7 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} +2 a^{-2} + a^{-4} -4 a^{-6} +2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +6 z^{10} a^{-8} +4 z^{10} a^{-10} +3 z^9 a^{-5} +4 z^9 a^{-7} +8 z^9 a^{-9} +7 z^9 a^{-11} +3 z^8 a^{-4} +3 z^8 a^{-6} -9 z^8 a^{-8} -2 z^8 a^{-10} +7 z^8 a^{-12} +2 z^7 a^{-3} -3 z^7 a^{-5} -5 z^7 a^{-7} -18 z^7 a^{-9} -14 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -6 z^6 a^{-4} -14 z^6 a^{-6} +6 z^6 a^{-8} -4 z^6 a^{-10} -16 z^6 a^{-12} +z^6 a^{-14} -5 z^5 a^{-3} -2 z^5 a^{-5} -4 z^5 a^{-7} +10 z^5 a^{-9} +8 z^5 a^{-11} -9 z^5 a^{-13} -4 z^4 a^{-2} +3 z^4 a^{-4} +21 z^4 a^{-6} +z^4 a^{-8} -3 z^4 a^{-10} +8 z^4 a^{-12} -2 z^4 a^{-14} +2 z^3 a^{-3} +3 z^3 a^{-5} +14 z^3 a^{-7} +4 z^3 a^{-9} -5 z^3 a^{-11} +4 z^3 a^{-13} +5 z^2 a^{-2} -2 z^2 a^{-4} -15 z^2 a^{-6} -2 z^2 a^{-8} +4 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} +z a^{-3} -2 z a^{-5} -7 z a^{-7} -3 z a^{-9} +z a^{-11} -2 a^{-2} + a^{-4} +4 a^{-6} +2 a^{-8} }[/math] |
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