K12a1006
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+18 q^2-25 q+31-32 q^{-1} +30 q^{-2} -24 q^{-3} +16 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+25 t^2-41 t+49-41 t^{-1} +25 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+5 z^4+z^2+1 }[/math] |
| Determinant | 205 |
| 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+5 a^2 z^4-3 z^4 a^{-2} +6 z^4-2 a^4 z^2+a^2 z^2-3 z^2 a^{-2} +5 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+7 a^4 z^{10}+16 a^2 z^{10}+9 z^{10}+7 a^5 z^9+6 a^3 z^9+13 a z^9+14 z^9 a^{-1} +4 a^6 z^8-18 a^4 z^8-43 a^2 z^8+14 z^8 a^{-2} -7 z^8+a^7 z^7-22 a^5 z^7-35 a^3 z^7-46 a z^7-25 z^7 a^{-1} +9 z^7 a^{-3} -13 a^6 z^6+15 a^4 z^6+46 a^2 z^6-26 z^6 a^{-2} +4 z^6 a^{-4} -12 z^6-3 a^7 z^5+21 a^5 z^5+43 a^3 z^5+50 a z^5+18 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4-10 a^4 z^4-27 a^2 z^4+22 z^4 a^{-2} -4 z^4 a^{-4} +20 z^4+2 a^7 z^3-8 a^5 z^3-26 a^3 z^3-25 a z^3-3 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} -a^6 z^2+4 a^4 z^2+3 a^2 z^2-8 z^2 a^{-2} -10 z^2+2 a^5 z+5 a^3 z+4 a z-z a^{-3} +a^2+ a^{-2} +3 }[/math] |
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