K12a1189
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+5 q^9-13 q^8+22 q^7-32 q^6+40 q^5-42 q^4+40 q^3-32 q^2+22 q-12+5 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-24 t^2+63 t-85+63 t^{-1} -24 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+3 z^2+1 }[/math] |
| Determinant | 267 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +2 z^4 a^{-4} -z^4 a^{-8} -z^4+z^2 a^{-2} +z^2 a^{-4} +z^2 a^{-6} + a^{-2} + a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{11} a^{-5} +5 z^{11} a^{-7} +15 z^{10} a^{-4} +27 z^{10} a^{-6} +12 z^{10} a^{-8} +21 z^9 a^{-3} +24 z^9 a^{-5} +14 z^9 a^{-7} +11 z^9 a^{-9} +19 z^8 a^{-2} -12 z^8 a^{-4} -63 z^8 a^{-6} -27 z^8 a^{-8} +5 z^8 a^{-10} +12 z^7 a^{-1} -32 z^7 a^{-3} -82 z^7 a^{-5} -69 z^7 a^{-7} -30 z^7 a^{-9} +z^7 a^{-11} -26 z^6 a^{-2} -19 z^6 a^{-4} +36 z^6 a^{-6} +12 z^6 a^{-8} -12 z^6 a^{-10} +5 z^6+a z^5-12 z^5 a^{-1} +14 z^5 a^{-3} +71 z^5 a^{-5} +70 z^5 a^{-7} +24 z^5 a^{-9} -2 z^5 a^{-11} +10 z^4 a^{-2} +21 z^4 a^{-4} +2 z^4 a^{-6} +z^4 a^{-8} +7 z^4 a^{-10} -3 z^4+2 z^3 a^{-1} -z^3 a^{-3} -18 z^3 a^{-5} -25 z^3 a^{-7} -9 z^3 a^{-9} +z^3 a^{-11} -4 z^2 a^{-4} -3 z^2 a^{-6} -z^2 a^{-10} +3 z a^{-7} +3 z a^{-9} - a^{-2} - a^{-6} - a^{-8} }[/math] |
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