K12a540
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-15 q^9+20 q^8-25 q^7+26 q^6-23 q^5+19 q^4-12 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+19 t^2-37 t+45-37 t^{-1} +19 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-5 z^4+3 z^2+1 }[/math] |
| Determinant | 165 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -5 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +3 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} +3 a^{-4} -2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +5 z^9 a^{-5} +9 z^9 a^{-7} +11 z^9 a^{-9} +7 z^9 a^{-11} +5 z^8 a^{-4} +3 z^8 a^{-6} -7 z^8 a^{-8} +2 z^8 a^{-10} +7 z^8 a^{-12} +3 z^7 a^{-3} -9 z^7 a^{-5} -23 z^7 a^{-7} -26 z^7 a^{-9} -11 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -13 z^6 a^{-4} -19 z^6 a^{-6} -5 z^6 a^{-8} -16 z^6 a^{-10} -15 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +6 z^5 a^{-5} +26 z^5 a^{-7} +21 z^5 a^{-9} -9 z^5 a^{-13} -3 z^4 a^{-2} +13 z^4 a^{-4} +27 z^4 a^{-6} +13 z^4 a^{-8} +11 z^4 a^{-10} +7 z^4 a^{-12} -2 z^4 a^{-14} +5 z^3 a^{-3} -3 z^3 a^{-5} -14 z^3 a^{-7} -8 z^3 a^{-9} +3 z^3 a^{-11} +5 z^3 a^{-13} +2 z^2 a^{-2} -9 z^2 a^{-4} -16 z^2 a^{-6} -5 z^2 a^{-8} -2 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} +4 z a^{-7} +4 z a^{-9} -z a^{-11} -z a^{-13} +3 a^{-4} +2 a^{-6} }[/math] |
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