K12n577
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+2 q^9-3 q^8+4 q^7-4 q^6+4 q^5-4 q^4+3 q^3-q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-3 t^2+6 t-7+6 t^{-1} -3 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+3 z^4+3 z^2+1 }[/math] |
| Determinant | 27 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-6} -z^4 a^{-4} +5 z^4 a^{-6} -z^4 a^{-8} +z^2 a^{-2} -3 z^2 a^{-4} +8 z^2 a^{-6} -3 z^2 a^{-8} +2 a^{-2} -3 a^{-4} +4 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +z^9 a^{-5} +3 z^9 a^{-7} +2 z^9 a^{-9} -6 z^8 a^{-6} -4 z^8 a^{-8} +2 z^8 a^{-10} -6 z^7 a^{-5} -17 z^7 a^{-7} -10 z^7 a^{-9} +z^7 a^{-11} +z^6 a^{-4} +14 z^6 a^{-6} +3 z^6 a^{-8} -10 z^6 a^{-10} +12 z^5 a^{-5} +31 z^5 a^{-7} +14 z^5 a^{-9} -5 z^5 a^{-11} -5 z^4 a^{-4} -20 z^4 a^{-6} -2 z^4 a^{-8} +13 z^4 a^{-10} -10 z^3 a^{-5} -25 z^3 a^{-7} -9 z^3 a^{-9} +6 z^3 a^{-11} +z^2 a^{-2} +8 z^2 a^{-4} +15 z^2 a^{-6} +3 z^2 a^{-8} -5 z^2 a^{-10} +z a^{-3} +4 z a^{-5} +7 z a^{-7} +3 z a^{-9} -z a^{-11} -2 a^{-2} -3 a^{-4} -4 a^{-6} -2 a^{-8} }[/math] |
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