K12a733
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-2 q^{11}+3 q^{10}-6 q^9+8 q^8-10 q^7+11 q^6-10 q^5+9 q^4-6 q^3+4 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+11 t^2-15 t+15-15 t^{-1} +11 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-7 z^4+2 z^2+1 }[/math] |
| Determinant | 73 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -3 z^4 a^{-4} -2 z^4 a^{-6} -4 z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} -z^2 a^{-4} +2 z^2 a^{-6} -5 z^2 a^{-8} +3 z^2 a^{-10} + a^{-2} +2 a^{-6} -3 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} +2 z^9 a^{-5} -3 z^9 a^{-7} -3 z^9 a^{-9} +2 z^9 a^{-11} +2 z^8 a^{-4} -9 z^8 a^{-6} -22 z^8 a^{-8} -9 z^8 a^{-10} +2 z^8 a^{-12} +2 z^7 a^{-3} -6 z^7 a^{-5} +z^7 a^{-7} +z^7 a^{-9} -6 z^7 a^{-11} +2 z^7 a^{-13} +z^6 a^{-2} -5 z^6 a^{-4} +19 z^6 a^{-6} +49 z^6 a^{-8} +17 z^6 a^{-10} -6 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +6 z^5 a^{-5} +11 z^5 a^{-7} +8 z^5 a^{-9} +2 z^5 a^{-11} -8 z^5 a^{-13} -4 z^4 a^{-2} -19 z^4 a^{-6} -44 z^4 a^{-8} -15 z^4 a^{-10} +2 z^4 a^{-12} -4 z^4 a^{-14} +5 z^3 a^{-3} -4 z^3 a^{-5} -12 z^3 a^{-7} -5 z^3 a^{-9} +6 z^3 a^{-11} +8 z^3 a^{-13} +4 z^2 a^{-2} +2 z^2 a^{-4} +8 z^2 a^{-6} +19 z^2 a^{-8} +7 z^2 a^{-10} +z^2 a^{-12} +3 z^2 a^{-14} +3 z a^{-7} +z a^{-9} -5 z a^{-11} -3 z a^{-13} - a^{-2} -2 a^{-6} -3 a^{-8} - a^{-10} }[/math] |
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