K12a178
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+7 q^3-11 q^2+16 q-20+21 q^{-1} -20 q^{-2} +17 q^{-3} -12 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-16 t^2+32 t-37+32 t^{-1} -16 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+2 z^4-5 z^2+1 }[/math] |
| Determinant | 139 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6+a^6-2 z^4 a^4-3 z^2 a^4+z^6 a^2-5 z^2 a^2-3 a^2+2 z^6+7 z^4+9 z^2+5-3 z^4 a^{-2} -8 z^2 a^{-2} -4 a^{-2} +z^2 a^{-4} +2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+3 z^{10} a^{-2} +7 z^{10}+8 a^3 z^9+12 a z^9+7 z^9 a^{-1} +3 z^9 a^{-3} +10 a^4 z^8+5 a^2 z^8-8 z^8 a^{-2} +z^8 a^{-4} -14 z^8+9 a^5 z^7-10 a^3 z^7-45 a z^7-40 z^7 a^{-1} -14 z^7 a^{-3} +6 a^6 z^6-16 a^4 z^6-38 a^2 z^6-6 z^6 a^{-2} -5 z^6 a^{-4} -17 z^6+3 a^7 z^5-13 a^5 z^5-5 a^3 z^5+44 a z^5+54 z^5 a^{-1} +21 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+8 a^4 z^4+40 a^2 z^4+28 z^4 a^{-2} +9 z^4 a^{-4} +44 z^4-2 a^7 z^3+10 a^5 z^3+5 a^3 z^3-20 a z^3-24 z^3 a^{-1} -11 z^3 a^{-3} -a^8 z^2+4 a^6 z^2-19 a^2 z^2-19 z^2 a^{-2} -7 z^2 a^{-4} -26 z^2-2 a^5 z+3 a z+3 z a^{-1} +2 z a^{-3} -a^6+3 a^2+4 a^{-2} +2 a^{-4} +5 }[/math] |
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