K12n538
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^8-5 q^7+7 q^6-10 q^5+11 q^4-10 q^3+9 q^2-6 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+10 t^2-11 t+11-11 t^{-1} +10 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+1 }[/math] |
| Determinant | 65 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -3 z^4 a^{-2} +7 z^4 a^{-4} -4 z^4 a^{-6} +3 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} +2 a^{-2} -2 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-3} +8 z^9 a^{-5} +3 z^9 a^{-7} +4 z^8 a^{-2} -z^8 a^{-4} -4 z^8 a^{-6} +z^8 a^{-8} +z^7 a^{-1} -20 z^7 a^{-3} -33 z^7 a^{-5} -12 z^7 a^{-7} -16 z^6 a^{-2} -21 z^6 a^{-4} -7 z^6 a^{-6} -2 z^6 a^{-8} -3 z^5 a^{-1} +19 z^5 a^{-3} +38 z^5 a^{-5} +17 z^5 a^{-7} +z^5 a^{-9} +15 z^4 a^{-2} +29 z^4 a^{-4} +18 z^4 a^{-6} +4 z^4 a^{-8} +z^3 a^{-1} -5 z^3 a^{-3} -15 z^3 a^{-5} -7 z^3 a^{-7} +2 z^3 a^{-9} -2 z^2 a^{-2} -9 z^2 a^{-4} -12 z^2 a^{-6} -3 z^2 a^{-8} +2 z^2 a^{-10} +2 z a^{-3} +2 z a^{-5} -2 z a^{-7} -2 z a^{-9} -2 a^{-2} +2 a^{-6} + a^{-8} }[/math] |
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