K12a200
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+10 q-17+26 q^{-1} -32 q^{-2} +34 q^{-3} -32 q^{-4} +26 q^{-5} -18 q^{-6} +10 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-24 t^2+47 t-57+47 t^{-1} -24 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-6 z^2 a^6-3 a^6+3 z^6 a^4+10 z^4 a^4+12 z^2 a^4+5 a^4-z^8 a^2-5 z^6 a^2-12 z^4 a^2-13 z^2 a^2-5 a^2+z^6+3 z^4+4 z^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^5 z^{11}+2 a^3 z^{11}+6 a^6 z^{10}+13 a^4 z^{10}+7 a^2 z^{10}+9 a^7 z^9+16 a^5 z^9+18 a^3 z^9+11 a z^9+8 a^8 z^8+4 a^6 z^8-14 a^4 z^8-a^2 z^8+9 z^8+4 a^9 z^7-12 a^7 z^7-38 a^5 z^7-52 a^3 z^7-26 a z^7+4 z^7 a^{-1} +a^{10} z^6-16 a^8 z^6-27 a^6 z^6-15 a^4 z^6-29 a^2 z^6+z^6 a^{-2} -23 z^6-8 a^9 z^5+29 a^5 z^5+53 a^3 z^5+24 a z^5-8 z^5 a^{-1} -2 a^{10} z^4+11 a^8 z^4+25 a^6 z^4+35 a^4 z^4+46 a^2 z^4-2 z^4 a^{-2} +21 z^4+5 a^9 z^3+2 a^7 z^3-12 a^5 z^3-20 a^3 z^3-9 a z^3+2 z^3 a^{-1} +a^{10} z^2-4 a^8 z^2-13 a^6 z^2-23 a^4 z^2-25 a^2 z^2-10 z^2-a^9 z+2 a^5 z+2 a^3 z+a z+a^8+3 a^6+5 a^4+5 a^2+3 }[/math] |
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