K12a444
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+5 q^{10}-10 q^9+15 q^8-18 q^7+20 q^6-19 q^5+16 q^4-11 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-30 t+39-30 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4+4 z^2+1 }[/math] |
| Determinant | 129 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -2 z^4 a^{-4} -z^4 a^{-6} +3 z^4 a^{-8} +2 z^2 a^{-2} -z^2 a^{-4} +6 z^2 a^{-8} -3 z^2 a^{-10} + a^{-2} - a^{-6} +4 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^{10} a^{-10} +4 z^9 a^{-5} +5 z^9 a^{-7} +5 z^9 a^{-9} +4 z^9 a^{-11} +4 z^8 a^{-4} -4 z^8 a^{-6} -16 z^8 a^{-8} -4 z^8 a^{-10} +4 z^8 a^{-12} +3 z^7 a^{-3} -6 z^7 a^{-5} -20 z^7 a^{-7} -22 z^7 a^{-9} -8 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -7 z^6 a^{-4} +4 z^6 a^{-6} +17 z^6 a^{-8} -7 z^6 a^{-10} -11 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +z^5 a^{-5} +35 z^5 a^{-7} +33 z^5 a^{-9} -3 z^5 a^{-11} -10 z^5 a^{-13} -3 z^4 a^{-2} -2 z^4 a^{-4} -6 z^4 a^{-6} +6 z^4 a^{-8} +23 z^4 a^{-10} +7 z^4 a^{-12} -3 z^4 a^{-14} +5 z^3 a^{-3} -4 z^3 a^{-5} -27 z^3 a^{-7} -12 z^3 a^{-9} +14 z^3 a^{-11} +8 z^3 a^{-13} +3 z^2 a^{-2} +4 z^2 a^{-4} -14 z^2 a^{-8} -17 z^2 a^{-10} -3 z^2 a^{-12} +z^2 a^{-14} +2 z a^{-5} +6 z a^{-7} -6 z a^{-11} -2 z a^{-13} - a^{-2} + a^{-6} +4 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
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