K12a885
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-13 q^6+24 q^5-35 q^4+43 q^3-46 q^2+43 q-34+24 q^{-1} -13 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-32 t^2+63 t-77+63 t^{-1} -32 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+2 z^4+1 }[/math] |
| Determinant | 287 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-4 z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-6} +4 z^4-a^2 z^2-2 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} +2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{11} a^{-1} +5 z^{11} a^{-3} +29 z^{10} a^{-2} +17 z^{10} a^{-4} +12 z^{10}+11 a z^9+20 z^9 a^{-1} +34 z^9 a^{-3} +25 z^9 a^{-5} +5 a^2 z^8-57 z^8 a^{-2} -9 z^8 a^{-4} +22 z^8 a^{-6} -21 z^8+a^3 z^7-28 a z^7-84 z^7 a^{-1} -108 z^7 a^{-3} -40 z^7 a^{-5} +13 z^7 a^{-7} -12 a^2 z^6+9 z^6 a^{-2} -34 z^6 a^{-4} -31 z^6 a^{-6} +5 z^6 a^{-8} -5 z^6-2 a^3 z^5+22 a z^5+82 z^5 a^{-1} +94 z^5 a^{-3} +23 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +9 a^2 z^4+26 z^4 a^{-2} +34 z^4 a^{-4} +16 z^4 a^{-6} -2 z^4 a^{-8} +19 z^4+a^3 z^3-8 a z^3-28 z^3 a^{-1} -30 z^3 a^{-3} -8 z^3 a^{-5} +3 z^3 a^{-7} -3 a^2 z^2-9 z^2 a^{-2} -9 z^2 a^{-4} -4 z^2 a^{-6} -7 z^2+a z+3 z a^{-1} +3 z a^{-3} +z a^{-5} +1 }[/math] |
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