K12n557
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^{10}-6 q^9+10 q^8-14 q^7+16 q^6-16 q^5+14 q^4-10 q^3+6 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+12 t^2-21 t+25-21 t^{-1} +12 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-6 z^4+1 }[/math] |
| Determinant | 97 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} +z^4 a^{-2} -2 z^4 a^{-4} -7 z^4 a^{-6} +2 z^4 a^{-8} +3 z^2 a^{-2} -7 z^2 a^{-6} +4 z^2 a^{-8} +2 a^{-2} -2 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +3 z^9 a^{-5} +6 z^9 a^{-7} +3 z^9 a^{-9} +3 z^8 a^{-4} +6 z^8 a^{-6} +6 z^8 a^{-8} +3 z^8 a^{-10} +2 z^7 a^{-3} -5 z^7 a^{-5} -10 z^7 a^{-7} -2 z^7 a^{-9} +z^7 a^{-11} +z^6 a^{-2} -6 z^6 a^{-4} -19 z^6 a^{-6} -13 z^6 a^{-8} -z^6 a^{-10} -5 z^5 a^{-3} +4 z^5 a^{-5} +8 z^5 a^{-7} +4 z^5 a^{-9} +5 z^5 a^{-11} -4 z^4 a^{-2} +2 z^4 a^{-4} +21 z^4 a^{-6} +12 z^4 a^{-8} +3 z^4 a^{-12} +2 z^3 a^{-3} -5 z^3 a^{-5} -5 z^3 a^{-7} -6 z^3 a^{-9} -8 z^3 a^{-11} +5 z^2 a^{-2} -12 z^2 a^{-6} -5 z^2 a^{-8} -z^2 a^{-10} -3 z^2 a^{-12} +z a^{-3} +z a^{-5} +z a^{-7} +3 z a^{-9} +2 z a^{-11} -2 a^{-2} +2 a^{-6} + a^{-8} }[/math] |
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