K12a792
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-5 q^5+7 q^4-10 q^3+12 q^2-12 q+12-9 q^{-1} +7 q^{-2} -4 q^{-3} +2 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^2-21 t+31-21 t^{-1} +6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^4+3 z^2+1 }[/math] |
| Determinant | 85 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^4-a^4+z^4 a^2+z^2 a^2+a^2+2 z^4+2 z^2+1+2 z^4 a^{-2} +2 z^2 a^{-2} + a^{-2} +z^4 a^{-4} - a^{-4} -z^2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +5 z^{10} a^{-2} +3 z^{10} a^{-4} +2 z^{10}+2 a z^9-z^9 a^{-1} +z^9 a^{-3} +4 z^9 a^{-5} +2 a^2 z^8-24 z^8 a^{-2} -12 z^8 a^{-4} +3 z^8 a^{-6} -7 z^8+2 a^3 z^7-4 a z^7-6 z^7 a^{-1} -19 z^7 a^{-3} -18 z^7 a^{-5} +z^7 a^{-7} +2 a^4 z^6-2 a^2 z^6+45 z^6 a^{-2} +14 z^6 a^{-4} -13 z^6 a^{-6} +14 z^6+a^5 z^5-2 a^3 z^5+5 a z^5+18 z^5 a^{-1} +37 z^5 a^{-3} +23 z^5 a^{-5} -4 z^5 a^{-7} -5 a^4 z^4-a^2 z^4-38 z^4 a^{-2} -10 z^4 a^{-4} +13 z^4 a^{-6} -11 z^4-3 a^5 z^3-3 a^3 z^3-a z^3-13 z^3 a^{-1} -27 z^3 a^{-3} -12 z^3 a^{-5} +3 z^3 a^{-7} +3 a^4 z^2+2 a^2 z^2+12 z^2 a^{-2} +5 z^2 a^{-4} -2 z^2 a^{-6} +4 z^2+2 a^5 z+2 a^3 z+2 z a^{-1} +5 z a^{-3} +3 z a^{-5} -a^4-a^2- a^{-2} - a^{-4} +1 }[/math] |
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