K12a983
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+10 q^{10}-19 q^9+27 q^8-34 q^7+37 q^6-34 q^5+28 q^4-19 q^3+11 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+25 t^2-52 t+65-52 t^{-1} +25 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-5 z^4+3 z^2+1 }[/math] |
| Determinant | 229 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -8 z^4 a^{-6} +z^4 a^{-10} +z^2 a^{-2} +6 z^2 a^{-4} -7 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} +3 a^{-4} -2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-7} +3 z^{11} a^{-9} +9 z^{10} a^{-6} +18 z^{10} a^{-8} +9 z^{10} a^{-10} +12 z^9 a^{-5} +18 z^9 a^{-7} +17 z^9 a^{-9} +11 z^9 a^{-11} +9 z^8 a^{-4} -7 z^8 a^{-6} -36 z^8 a^{-8} -12 z^8 a^{-10} +8 z^8 a^{-12} +4 z^7 a^{-3} -25 z^7 a^{-5} -61 z^7 a^{-7} -59 z^7 a^{-9} -23 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -19 z^6 a^{-4} -19 z^6 a^{-6} +21 z^6 a^{-8} +4 z^6 a^{-10} -15 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +19 z^5 a^{-5} +70 z^5 a^{-7} +74 z^5 a^{-9} +22 z^5 a^{-11} -8 z^5 a^{-13} -2 z^4 a^{-2} +15 z^4 a^{-4} +32 z^4 a^{-6} +5 z^4 a^{-8} -z^4 a^{-10} +7 z^4 a^{-12} -2 z^4 a^{-14} +2 z^3 a^{-3} -9 z^3 a^{-5} -34 z^3 a^{-7} -43 z^3 a^{-9} -16 z^3 a^{-11} +4 z^3 a^{-13} +z^2 a^{-2} -11 z^2 a^{-4} -16 z^2 a^{-6} -3 z^2 a^{-8} -z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +8 z a^{-7} +10 z a^{-9} +3 z a^{-11} +3 a^{-4} +2 a^{-6} }[/math] |
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