K12a243
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-7 q^5+11 q^4-16 q^3+19 q^2-20 q+19-15 q^{-1} +11 q^{-2} -6 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+12 t^2-31 t+43-31 t^{-1} +12 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-z^2+1 }[/math] |
| Determinant | 133 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+2 a^2 z^4-2 z^4 a^{-2} +2 z^4 a^{-4} -2 z^4-a^4 z^2+4 a^2 z^2-3 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} -3 z^2-a^4+3 a^2- a^{-2} + a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +7 z^{10} a^{-2} +4 z^{10} a^{-4} +3 z^{10}+4 a z^9+7 z^9 a^{-1} +9 z^9 a^{-3} +6 z^9 a^{-5} +4 a^2 z^8-18 z^8 a^{-2} -8 z^8 a^{-4} +4 z^8 a^{-6} -2 z^8+4 a^3 z^7-3 a z^7-27 z^7 a^{-1} -44 z^7 a^{-3} -23 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6+9 z^6 a^{-2} -10 z^6 a^{-4} -15 z^6 a^{-6} +z^6+a^5 z^5-4 a^3 z^5+2 a z^5+38 z^5 a^{-1} +58 z^5 a^{-3} +24 z^5 a^{-5} -3 z^5 a^{-7} -6 a^4 z^4-10 a^2 z^4+10 z^4 a^{-2} +22 z^4 a^{-4} +13 z^4 a^{-6} -3 z^4-2 a^5 z^3-2 a^3 z^3-5 a z^3-23 z^3 a^{-1} -27 z^3 a^{-3} -8 z^3 a^{-5} +z^3 a^{-7} +4 a^4 z^2+9 a^2 z^2-9 z^2 a^{-2} -9 z^2 a^{-4} -2 z^2 a^{-6} +3 z^2+a^5 z+2 a^3 z+3 a z+5 z a^{-1} +3 z a^{-3} -a^4-3 a^2+ a^{-2} + a^{-4} -1 }[/math] |
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