K12a676
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-8 q^8+12 q^7-17 q^6+20 q^5-21 q^4+20 q^3-15 q^2+11 q-6+3 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-14 t^2+32 t-41+32 t^{-1} -14 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 139 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^6 a^{-6} +3 z^4 a^{-2} +z^4 a^{-4} +2 z^4 a^{-6} -z^4 a^{-8} -z^4+5 z^2 a^{-2} +z^2 a^{-6} -z^2 a^{-8} -2 z^2+3 a^{-2} - a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +4 z^{10} a^{-4} +10 z^{10} a^{-6} +6 z^{10} a^{-8} +4 z^9 a^{-3} +z^9 a^{-5} +4 z^9 a^{-7} +7 z^9 a^{-9} +4 z^8 a^{-2} -8 z^8 a^{-4} -36 z^8 a^{-6} -20 z^8 a^{-8} +4 z^8 a^{-10} +4 z^7 a^{-1} -2 z^7 a^{-3} -13 z^7 a^{-5} -35 z^7 a^{-7} -27 z^7 a^{-9} +z^7 a^{-11} +14 z^6 a^{-4} +47 z^6 a^{-6} +16 z^6 a^{-8} -14 z^6 a^{-10} +3 z^6+a z^5-4 z^5 a^{-1} -2 z^5 a^{-3} +20 z^5 a^{-5} +48 z^5 a^{-7} +28 z^5 a^{-9} -3 z^5 a^{-11} -10 z^4 a^{-2} -15 z^4 a^{-4} -25 z^4 a^{-6} -4 z^4 a^{-8} +10 z^4 a^{-10} -6 z^4-2 a z^3-2 z^3 a^{-1} -z^3 a^{-3} -9 z^3 a^{-5} -19 z^3 a^{-7} -10 z^3 a^{-9} +z^3 a^{-11} +9 z^2 a^{-2} +6 z^2 a^{-4} +4 z^2 a^{-6} +2 z^2 a^{-8} -z^2 a^{-10} +4 z^2+a z+2 z a^{-1} +2 z a^{-3} +z a^{-9} -3 a^{-2} + a^{-6} -1 }[/math] |
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