K12a159
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+6 q^{10}-12 q^9+17 q^8-22 q^7+25 q^6-23 q^5+20 q^4-14 q^3+9 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-37 t+49-37 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4+5 z^2+1 }[/math] |
| Determinant | 157 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -z^4 a^{-4} +3 z^4 a^{-8} +z^2 a^{-2} +z^2 a^{-4} +2 z^2 a^{-6} +4 z^2 a^{-8} -3 z^2 a^{-10} + a^{-4} + a^{-6} + a^{-8} -3 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +4 z^{10} a^{-6} +7 z^{10} a^{-8} +3 z^{10} a^{-10} +7 z^9 a^{-5} +11 z^9 a^{-7} +8 z^9 a^{-9} +4 z^9 a^{-11} +7 z^8 a^{-4} +z^8 a^{-6} -10 z^8 a^{-8} +4 z^8 a^{-12} +4 z^7 a^{-3} -13 z^7 a^{-5} -33 z^7 a^{-7} -23 z^7 a^{-9} -4 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -16 z^6 a^{-4} -18 z^6 a^{-6} -2 z^6 a^{-8} -10 z^6 a^{-10} -8 z^6 a^{-12} +z^6 a^{-14} -9 z^5 a^{-3} +5 z^5 a^{-5} +38 z^5 a^{-7} +25 z^5 a^{-9} -8 z^5 a^{-11} -9 z^5 a^{-13} -2 z^4 a^{-2} +9 z^4 a^{-4} +18 z^4 a^{-6} +17 z^4 a^{-8} +15 z^4 a^{-10} +2 z^4 a^{-12} -3 z^4 a^{-14} +4 z^3 a^{-3} -3 z^3 a^{-5} -19 z^3 a^{-7} -6 z^3 a^{-9} +14 z^3 a^{-11} +8 z^3 a^{-13} +z^2 a^{-2} -4 z^2 a^{-4} -5 z^2 a^{-6} -8 z^2 a^{-8} -10 z^2 a^{-10} +2 z^2 a^{-14} +z a^{-5} +5 z a^{-7} -z a^{-9} -8 z a^{-11} -3 z a^{-13} + a^{-4} - a^{-6} + a^{-8} +3 a^{-10} + a^{-12} }[/math] |
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