K12a177
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-3 q^2+8 q-15+21 q^{-1} -25 q^{-2} +28 q^{-3} -25 q^{-4} +20 q^{-5} -14 q^{-6} +7 q^{-7} -3 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-15 t^2+41 t-55+41 t^{-1} -15 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^4-z^2+1 }[/math] |
| Determinant | 171 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-2 z^4 a^6-3 z^2 a^6-3 a^6+z^6 a^4+z^4 a^4+3 z^2 a^4+3 a^4+z^6 a^2-z^2 a^2-2 z^4-2 z^2-1+z^2 a^{-2} + a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+4 a^6 z^{10}+8 a^4 z^{10}+4 a^2 z^{10}+6 a^7 z^9+13 a^5 z^9+13 a^3 z^9+6 a z^9+5 a^8 z^8-9 a^4 z^8+a^2 z^8+5 z^8+3 a^9 z^7-12 a^7 z^7-39 a^5 z^7-36 a^3 z^7-9 a z^7+3 z^7 a^{-1} +a^{10} z^6-11 a^8 z^6-14 a^6 z^6-3 a^4 z^6-10 a^2 z^6+z^6 a^{-2} -8 z^6-8 a^9 z^5+9 a^7 z^5+50 a^5 z^5+45 a^3 z^5+5 a z^5-7 z^5 a^{-1} -3 a^{10} z^4+7 a^8 z^4+20 a^6 z^4+11 a^4 z^4+4 a^2 z^4-3 z^4 a^{-2} +6 a^9 z^3-2 a^7 z^3-27 a^5 z^3-30 a^3 z^3-6 a z^3+5 z^3 a^{-1} +2 a^{10} z^2-3 a^8 z^2-10 a^6 z^2-6 a^4 z^2+3 z^2 a^{-2} +4 z^2-2 a^9 z-2 a^7 z+4 a^5 z+6 a^3 z+a z-z a^{-1} +a^8+3 a^6+3 a^4- a^{-2} -1 }[/math] |
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