K12a957
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+17 q^{-1} -24 q^{-2} +30 q^{-3} -32 q^{-4} +30 q^{-5} -24 q^{-6} +17 q^{-7} -10 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-20 t^2+47 t-61+47 t^{-1} -20 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 203 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8-a^8+z^6 a^6+z^4 a^6+z^2 a^6+a^6+2 z^6 a^4+4 z^4 a^4+3 z^2 a^4+z^6 a^2+z^4 a^2+z^2 a^2+a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+2 z^3 a^{11}+4 z^8 a^{10}-12 z^6 a^{10}+9 z^4 a^{10}-2 z^2 a^{10}+8 z^9 a^9-26 z^7 a^9+27 z^5 a^9-16 z^3 a^9+5 z a^9+8 z^{10} a^8-21 z^8 a^8+14 z^6 a^8-6 z^4 a^8+3 z^2 a^8-a^8+3 z^{11} a^7+10 z^9 a^7-56 z^7 a^7+74 z^5 a^7-43 z^3 a^7+9 z a^7+17 z^{10} a^6-46 z^8 a^6+38 z^6 a^6-9 z^4 a^6+z^2 a^6-a^6+3 z^{11} a^5+15 z^9 a^5-62 z^7 a^5+77 z^5 a^5-37 z^3 a^5+6 z a^5+9 z^{10} a^4-9 z^8 a^4-12 z^6 a^4+24 z^4 a^4-8 z^2 a^4+13 z^9 a^3-25 z^7 a^3+22 z^5 a^3-9 z^3 a^3+2 z a^3+12 z^8 a^2-20 z^6 a^2+13 z^4 a^2-3 z^2 a^2-a^2+8 z^7 a-10 z^5 a+2 z^3 a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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