K12a581
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-6+11 q^{-1} -15 q^{-2} +18 q^{-3} -18 q^{-4} +17 q^{-5} -13 q^{-6} +9 q^{-7} -5 q^{-8} +2 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-14 t^2+26 t-31+26 t^{-1} -14 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+10 z^4+6 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-2 a^8+z^6 a^6+3 z^4 a^6+3 z^2 a^6+a^6+2 z^6 a^4+7 z^4 a^4+8 z^2 a^4+3 a^4+z^6 a^2+2 z^4 a^2-a^2-z^4-2 z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+8 z^3 a^{11}-4 z a^{11}+2 z^8 a^{10}-8 z^6 a^{10}+9 z^4 a^{10}-2 z^2 a^{10}+2 z^9 a^9-4 z^7 a^9-4 z^5 a^9+9 z^3 a^9-2 z a^9+2 z^{10} a^8-5 z^8 a^8+8 z^6 a^8-17 z^4 a^8+13 z^2 a^8-2 a^8+z^{11} a^7-z^7 a^7-z^5 a^7-6 z^3 a^7+3 z a^7+5 z^{10} a^6-16 z^8 a^6+31 z^6 a^6-34 z^4 a^6+11 z^2 a^6-a^6+z^{11} a^5+3 z^9 a^5-10 z^7 a^5+16 z^5 a^5-12 z^3 a^5+z a^5+3 z^{10} a^4-3 z^8 a^4-z^6 a^4+11 z^4 a^4-10 z^2 a^4+3 a^4+5 z^9 a^3-9 z^7 a^3+7 z^5 a^3+3 z^3 a^3-z a^3+6 z^8 a^2-13 z^6 a^2+13 z^4 a^2-4 z^2 a^2+a^2+5 z^7 a-10 z^5 a+6 z^3 a-z a+3 z^6-6 z^4+2 z^2+z^5 a^{-1} -2 z^3 a^{-1} }[/math] |
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