K12a738
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-5+10 q^{-1} -14 q^{-2} +17 q^{-3} -18 q^{-4} +17 q^{-5} -14 q^{-6} +10 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-13 t^2+27 t-33+27 t^{-1} -13 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+5 z^4+2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+3 z^4 a^6+4 z^2 a^6+2 a^6+z^6 a^4+z^4 a^4-2 z^2 a^4-2 a^4+z^6 a^2+3 z^4 a^2+4 z^2 a^2+2 a^2-z^4-2 z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+13 z^4 a^{10}-4 z^2 a^{10}+4 z^9 a^9-14 z^7 a^9+12 z^5 a^9-3 z^3 a^9+z a^9+3 z^{10} a^8-7 z^8 a^8+2 z^4 a^8+2 z^2 a^8-a^8+z^{11} a^7+4 z^9 a^7-22 z^7 a^7+30 z^5 a^7-20 z^3 a^7+5 z a^7+6 z^{10} a^6-20 z^8 a^6+31 z^6 a^6-28 z^4 a^6+11 z^2 a^6-2 a^6+z^{11} a^5+4 z^9 a^5-18 z^7 a^5+31 z^5 a^5-23 z^3 a^5+5 z a^5+3 z^{10} a^4-6 z^8 a^4+12 z^6 a^4-13 z^4 a^4+8 z^2 a^4-2 a^4+4 z^9 a^3-7 z^7 a^3+9 z^5 a^3-5 z^3 a^3+2 z a^3+4 z^8 a^2-4 z^6 a^2-3 z^4 a^2+7 z^2 a^2-2 a^2+4 z^7 a-7 z^5 a+3 z^3 a+3 z^6-7 z^4+4 z^2+z^5 a^{-1} -2 z^3 a^{-1} }[/math] |
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