K12a1133
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-6 q^2+12 q-17+22 q^{-1} -25 q^{-2} +24 q^{-3} -20 q^{-4} +15 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-18 t^2+36 t-43+36 t^{-1} -18 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+6 z^4+1 }[/math] |
| Determinant | 159 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-z^2 a^6+z^6 a^4+z^4 a^4-z^2 a^4+2 z^6 a^2+5 z^4 a^2+3 z^2 a^2+z^6+2 z^4+z^2+1-z^4 a^{-2} -2 z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+7 a^2 z^{10}+3 z^{10}+8 a^5 z^9+11 a^3 z^9+7 a z^9+4 z^9 a^{-1} +10 a^6 z^8+5 a^4 z^8-12 a^2 z^8+3 z^8 a^{-2} -4 z^8+8 a^7 z^7-8 a^5 z^7-27 a^3 z^7-25 a z^7-13 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-16 a^6 z^6-20 a^4 z^6+6 a^2 z^6-12 z^6 a^{-2} -6 z^6+a^9 z^5-12 a^7 z^5-a^5 z^5+23 a^3 z^5+28 a z^5+13 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+10 a^6 z^4+16 a^4 z^4-4 a^2 z^4+15 z^4 a^{-2} +10 z^4-a^9 z^3+5 a^7 z^3+4 a^5 z^3-10 a^3 z^3-18 a z^3-6 z^3 a^{-1} +4 z^3 a^{-3} +a^8 z^2-3 a^6 z^2-3 a^4 z^2+a^2 z^2-6 z^2 a^{-2} -6 z^2-a^7 z-a^5 z+3 a^3 z+5 a z+2 z a^{-1} +1 }[/math] |
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