K12a329
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+8 q^{10}-13 q^9+18 q^8-21 q^7+22 q^6-20 q^5+15 q^4-10 q^3+6 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+17 t^2-31 t+37-31 t^{-1} +17 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-7 z^4+z^2+1 }[/math] |
| Determinant | 141 |
| 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} -6 z^2 a^{-6} +3 z^2 a^{-8} +z^2 a^{-10} +2 a^{-2} -3 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} +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} +2 z^8 a^{-6} -11 z^8 a^{-8} -3 z^8 a^{-10} +7 z^8 a^{-12} +2 z^7 a^{-3} -4 z^7 a^{-5} -11 z^7 a^{-7} -26 z^7 a^{-9} -17 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -6 z^6 a^{-4} -12 z^6 a^{-6} +4 z^6 a^{-8} -11 z^6 a^{-10} -19 z^6 a^{-12} +z^6 a^{-14} -5 z^5 a^{-3} +2 z^5 a^{-5} +16 z^5 a^{-7} +30 z^5 a^{-9} +11 z^5 a^{-11} -10 z^5 a^{-13} -4 z^4 a^{-2} +2 z^4 a^{-4} +19 z^4 a^{-6} +16 z^4 a^{-8} +18 z^4 a^{-10} +13 z^4 a^{-12} -2 z^4 a^{-14} +2 z^3 a^{-3} -5 z^3 a^{-5} -12 z^3 a^{-7} -11 z^3 a^{-9} -2 z^3 a^{-11} +4 z^3 a^{-13} +5 z^2 a^{-2} -15 z^2 a^{-6} -15 z^2 a^{-8} -8 z^2 a^{-10} -3 z^2 a^{-12} +z a^{-3} +3 z a^{-5} +4 z a^{-7} +2 z a^{-9} -2 a^{-2} +3 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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