K12n765
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^{10}-7 q^9+13 q^8-19 q^7+22 q^6-23 q^5+21 q^4-15 q^3+10 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+15 t^2-31 t+39-31 t^{-1} +15 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-3 z^4+2 z^2+1 }[/math] |
| Determinant | 137 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} +z^4 a^{-2} -6 z^4 a^{-6} +2 z^4 a^{-8} +z^2 a^{-2} +5 z^2 a^{-4} -7 z^2 a^{-6} +3 z^2 a^{-8} +4 a^{-4} -4 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-6} +3 z^{10} a^{-8} +8 z^9 a^{-5} +15 z^9 a^{-7} +7 z^9 a^{-9} +8 z^8 a^{-4} +10 z^8 a^{-6} +7 z^8 a^{-8} +5 z^8 a^{-10} +4 z^7 a^{-3} -15 z^7 a^{-5} -34 z^7 a^{-7} -14 z^7 a^{-9} +z^7 a^{-11} +z^6 a^{-2} -19 z^6 a^{-4} -41 z^6 a^{-6} -26 z^6 a^{-8} -5 z^6 a^{-10} -8 z^5 a^{-3} +5 z^5 a^{-5} +27 z^5 a^{-7} +21 z^5 a^{-9} +7 z^5 a^{-11} -2 z^4 a^{-2} +15 z^4 a^{-4} +42 z^4 a^{-6} +29 z^4 a^{-8} +7 z^4 a^{-10} +3 z^4 a^{-12} +3 z^3 a^{-3} -8 z^3 a^{-7} -14 z^3 a^{-9} -9 z^3 a^{-11} +z^2 a^{-2} -10 z^2 a^{-4} -20 z^2 a^{-6} -11 z^2 a^{-8} -5 z^2 a^{-10} -3 z^2 a^{-12} -2 z a^{-5} +4 z a^{-9} +2 z a^{-11} +4 a^{-4} +4 a^{-6} + a^{-8} }[/math] |
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