K12n667
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+3 q^9-6 q^8+9 q^7-11 q^6+12 q^5-12 q^4+10 q^3-6 q^2+4 q-1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-8 t^2+17 t-21+17 t^{-1} -8 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 75 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-4} +z^6 a^{-6} -z^4 a^{-2} +3 z^4 a^{-4} +3 z^4 a^{-6} -z^4 a^{-8} -z^2 a^{-2} +3 z^2 a^{-4} +3 z^2 a^{-6} -2 z^2 a^{-8} + a^{-2} + a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +5 z^9 a^{-7} +3 z^9 a^{-9} +2 z^8 a^{-4} +3 z^8 a^{-6} +4 z^8 a^{-8} +3 z^8 a^{-10} +z^7 a^{-3} -10 z^7 a^{-7} -8 z^7 a^{-9} +z^7 a^{-11} -z^6 a^{-4} -11 z^6 a^{-6} -22 z^6 a^{-8} -12 z^6 a^{-10} +2 z^5 a^{-3} -7 z^5 a^{-5} -6 z^5 a^{-7} -z^5 a^{-9} -4 z^5 a^{-11} +4 z^4 a^{-2} +2 z^4 a^{-4} +3 z^4 a^{-6} +19 z^4 a^{-8} +14 z^4 a^{-10} +z^3 a^{-1} +7 z^3 a^{-5} +12 z^3 a^{-7} +9 z^3 a^{-9} +5 z^3 a^{-11} -2 z^2 a^{-2} -2 z^2 a^{-4} +3 z^2 a^{-6} -2 z^2 a^{-8} -5 z^2 a^{-10} -2 z a^{-5} -3 z a^{-7} -3 z a^{-9} -2 z a^{-11} - a^{-2} - a^{-6} - a^{-8} }[/math] |
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