K12a1132
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-6 q^2+11 q-15+19 q^{-1} -20 q^{-2} +19 q^{-3} -16 q^{-4} +11 q^{-5} -6 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-16 t^2+29 t-33+29 t^{-1} -16 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+8 z^4+z^2+1 }[/math] |
| Determinant | 131 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6+z^6 a^4+2 z^4 a^4-a^4+2 z^6 a^2+6 z^4 a^2+5 z^2 a^2+2 a^2+z^6+2 z^4-z^4 a^{-2} -2 z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+5 a^5 z^9+5 a^3 z^9+4 a z^9+4 z^9 a^{-1} +6 a^6 z^8-a^4 z^8-17 a^2 z^8+3 z^8 a^{-2} -7 z^8+5 a^7 z^7-7 a^5 z^7-14 a^3 z^7-17 a z^7-14 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-12 a^6 z^6-3 a^4 z^6+29 a^2 z^6-12 z^6 a^{-2} +5 z^6+a^9 z^5-10 a^7 z^5+2 a^5 z^5+15 a^3 z^5+21 a z^5+15 z^5 a^{-1} -4 z^5 a^{-3} -6 a^8 z^4+11 a^6 z^4+3 a^4 z^4-35 a^2 z^4+14 z^4 a^{-2} -7 z^4-2 a^9 z^3+7 a^7 z^3+8 a^5 z^3-8 a^3 z^3-18 a z^3-7 z^3 a^{-1} +4 z^3 a^{-3} +2 a^8 z^2-2 a^6 z^2+3 a^4 z^2+15 a^2 z^2-4 z^2 a^{-2} +4 z^2-2 a^7 z-3 a^5 z+a^3 z+4 a z+2 z a^{-1} -a^4-2 a^2 }[/math] |
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