K12a570
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-11+18 q^{-1} -25 q^{-2} +30 q^{-3} -30 q^{-4} +28 q^{-5} -21 q^{-6} +14 q^{-7} -8 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-15 t^2+47 t-67+47 t^{-1} -15 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^4+5 z^2+1 }[/math] |
| Determinant | 195 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+3 z^2 a^8+a^8-3 z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+2 z^2 a^4+2 a^4+z^6 a^2+z^4 a^2+2 z^2 a^2-z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-10 z^6 a^{10}+10 z^4 a^{10}-4 z^2 a^{10}+a^{10}+5 z^9 a^9-15 z^7 a^9+15 z^5 a^9-9 z^3 a^9+4 z a^9+4 z^{10} a^8-3 z^8 a^8-16 z^6 a^8+24 z^4 a^8-11 z^2 a^8+a^8+z^{11} a^7+15 z^9 a^7-52 z^7 a^7+63 z^5 a^7-38 z^3 a^7+10 z a^7+9 z^{10} a^6-3 z^8 a^6-39 z^6 a^6+54 z^4 a^6-23 z^2 a^6+a^6+z^{11} a^5+21 z^9 a^5-51 z^7 a^5+41 z^5 a^5-17 z^3 a^5+5 z a^5+5 z^{10} a^4+17 z^8 a^4-56 z^6 a^4+49 z^4 a^4-17 z^2 a^4+2 a^4+11 z^9 a^3-4 z^7 a^3-18 z^5 a^3+11 z^3 a^3+z a^3+14 z^8 a^2-18 z^6 a^2+5 z^4 a^2-z^2 a^2+11 z^7 a-14 z^5 a+4 z^3 a+5 z^6-4 z^4+z^5 a^{-1} }[/math] |
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