K12a979
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+18 q^2-27 q+34-35 q^{-1} +34 q^{-2} -27 q^{-3} +19 q^{-4} -11 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+27 t^2-46 t+55-46 t^{-1} +27 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+7 z^4+4 z^2+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+4 a^2 z^6-z^6 a^{-2} +4 z^6-3 a^4 z^4+7 a^2 z^4-3 z^4 a^{-2} +6 z^4-4 a^4 z^2+8 a^2 z^2-3 z^2 a^{-2} +3 z^2-3 a^4+5 a^2- a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+8 a^4 z^{10}+18 a^2 z^{10}+10 z^{10}+8 a^5 z^9+14 a^3 z^9+21 a z^9+15 z^9 a^{-1} +4 a^6 z^8-15 a^4 z^8-37 a^2 z^8+14 z^8 a^{-2} -4 z^8+a^7 z^7-22 a^5 z^7-58 a^3 z^7-69 a z^7-25 z^7 a^{-1} +9 z^7 a^{-3} -11 a^6 z^6+a^4 z^6+13 a^2 z^6-24 z^6 a^{-2} +4 z^6 a^{-4} -27 z^6-3 a^7 z^5+19 a^5 z^5+62 a^3 z^5+68 a z^5+15 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4+a^4 z^4+4 a^2 z^4+20 z^4 a^{-2} -4 z^4 a^{-4} +36 z^4+3 a^7 z^3-10 a^5 z^3-35 a^3 z^3-28 a z^3+z^3 a^{-1} +6 z^3 a^{-3} -z^3 a^{-5} -2 a^6 z^2+4 a^4 z^2+3 a^2 z^2-8 z^2 a^{-2} -11 z^2-a^7 z+4 a^5 z+10 a^3 z+6 a z-z a^{-1} -2 z a^{-3} -3 a^4-5 a^2+ a^{-2} }[/math] |
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