K12a1197
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-10 q^5+18 q^4-27 q^3+35 q^2-37 q+36-30 q^{-1} +21 q^{-2} -12 q^{-3} +5 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+29 t^2-48 t+57-48 t^{-1} +29 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 237 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +3 z^6-2 a^2 z^4+7 z^4 a^{-2} -3 z^4 a^{-4} +z^4+8 z^2 a^{-2} -3 z^2 a^{-4} -4 z^2+a^2+5 a^{-2} -2 a^{-4} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-1} +4 z^{11} a^{-3} +21 z^{10} a^{-2} +9 z^{10} a^{-4} +12 z^{10}+18 a z^9+17 z^9 a^{-1} +7 z^9 a^{-3} +8 z^9 a^{-5} +18 a^2 z^8-55 z^8 a^{-2} -25 z^8 a^{-4} +4 z^8 a^{-6} -8 z^8+12 a^3 z^7-24 a z^7-54 z^7 a^{-1} -44 z^7 a^{-3} -25 z^7 a^{-5} +z^7 a^{-7} +5 a^4 z^6-25 a^2 z^6+56 z^6 a^{-2} +26 z^6 a^{-4} -12 z^6 a^{-6} -12 z^6+a^5 z^5-13 a^3 z^5+4 a z^5+43 z^5 a^{-1} +54 z^5 a^{-3} +26 z^5 a^{-5} -3 z^5 a^{-7} -3 a^4 z^4+9 a^2 z^4-36 z^4 a^{-2} -18 z^4 a^{-4} +9 z^4 a^{-6} +3 z^4+3 a^3 z^3+3 a z^3-12 z^3 a^{-1} -27 z^3 a^{-3} -13 z^3 a^{-5} +2 z^3 a^{-7} +17 z^2 a^{-2} +8 z^2 a^{-4} -z^2 a^{-6} +8 z^2+2 z a^{-1} +5 z a^{-3} +3 z a^{-5} -a^2-5 a^{-2} -2 a^{-4} -3 }[/math] |
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