K12n508
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^9+4 q^8-8 q^7+10 q^6-13 q^5+14 q^4-11 q^3+10 q^2-6 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+10 t^2-16 t+19-16 t^{-1} +10 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+6 z^4+4 z^2+1 }[/math] |
| Determinant | 81 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} +14 z^4 a^{-4} -4 z^4 a^{-6} -5 z^2 a^{-2} +16 z^2 a^{-4} -7 z^2 a^{-6} -2 a^{-2} +8 a^{-4} -6 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +3 z^9 a^{-3} +6 z^9 a^{-5} +3 z^9 a^{-7} +3 z^8 a^{-2} +6 z^8 a^{-4} +6 z^8 a^{-6} +3 z^8 a^{-8} +z^7 a^{-1} -7 z^7 a^{-3} -13 z^7 a^{-5} -4 z^7 a^{-7} +z^7 a^{-9} -12 z^6 a^{-2} -32 z^6 a^{-4} -24 z^6 a^{-6} -4 z^6 a^{-8} -4 z^5 a^{-1} -5 z^5 a^{-3} -5 z^5 a^{-5} +4 z^5 a^{-9} +15 z^4 a^{-2} +39 z^4 a^{-4} +25 z^4 a^{-6} +5 z^4 a^{-8} +4 z^4 a^{-10} +5 z^3 a^{-1} +15 z^3 a^{-3} +18 z^3 a^{-5} +4 z^3 a^{-7} -3 z^3 a^{-9} +z^3 a^{-11} -8 z^2 a^{-2} -22 z^2 a^{-4} -15 z^2 a^{-6} -2 z^2 a^{-8} -z^2 a^{-10} -2 z a^{-1} -6 z a^{-3} -10 z a^{-5} -6 z a^{-7} +2 a^{-2} +8 a^{-4} +6 a^{-6} + a^{-8} }[/math] |
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