K12a1158
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-2 q^9+4 q^8-7 q^7+9 q^6-11 q^5+11 q^4-10 q^3+9 q^2-6 q+4-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+12 t^2-15 t+15-15 t^{-1} +12 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-12 z^4-3 z^2+1 }[/math] |
| Determinant | 77 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -2 z^6 a^{-4} -z^6 a^{-6} -3 z^4 a^{-2} -8 z^4 a^{-4} -3 z^4 a^{-6} +z^4 a^{-8} +z^4-8 z^2 a^{-4} -z^2 a^{-6} +3 z^2 a^{-8} +3 z^2+2 a^{-2} -3 a^{-4} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10} a^{-6} +2 z^9 a^{-1} -3 z^9 a^{-3} -2 z^9 a^{-5} +3 z^9 a^{-7} -10 z^8 a^{-2} -20 z^8 a^{-4} -5 z^8 a^{-6} +4 z^8 a^{-8} +z^8-11 z^7 a^{-1} +z^7 a^{-3} +z^7 a^{-5} -7 z^7 a^{-7} +4 z^7 a^{-9} +16 z^6 a^{-2} +41 z^6 a^{-4} +5 z^6 a^{-6} -11 z^6 a^{-8} +3 z^6 a^{-10} -6 z^6+18 z^5 a^{-1} -2 z^5 a^{-5} +4 z^5 a^{-7} -10 z^5 a^{-9} +2 z^5 a^{-11} -12 z^4 a^{-2} -48 z^4 a^{-4} -5 z^4 a^{-6} +14 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +11 z^4-8 z^3 a^{-1} -3 z^3 a^{-5} +5 z^3 a^{-7} +13 z^3 a^{-9} -3 z^3 a^{-11} +7 z^2 a^{-2} +23 z^2 a^{-4} +z^2 a^{-6} -4 z^2 a^{-8} +3 z^2 a^{-10} -2 z^2 a^{-12} -6 z^2+z a^{-3} +z a^{-5} -4 z a^{-7} -4 z a^{-9} -2 a^{-2} -3 a^{-4} + a^{-8} +1 }[/math] |
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