K12a1237
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+17 q^2-26 q+33-35 q^{-1} +34 q^{-2} -28 q^{-3} +20 q^{-4} -12 q^{-5} +5 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+28 t^2-45 t+53-45 t^{-1} +28 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+2 z^4+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+3 a^2 z^6-z^6 a^{-2} +4 z^6-2 a^4 z^4+a^2 z^4-3 z^4 a^{-2} +6 z^4-2 a^2 z^2-2 z^2 a^{-2} +4 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^3 z^{11}+4 a z^{11}+10 a^4 z^{10}+21 a^2 z^{10}+11 z^{10}+10 a^5 z^9+10 a^3 z^9+14 a z^9+14 z^9 a^{-1} +5 a^6 z^8-23 a^4 z^8-56 a^2 z^8+12 z^8 a^{-2} -16 z^8+a^7 z^7-28 a^5 z^7-53 a^3 z^7-58 a z^7-26 z^7 a^{-1} +8 z^7 a^{-3} -13 a^6 z^6+10 a^4 z^6+49 a^2 z^6-18 z^6 a^{-2} +4 z^6 a^{-4} +4 z^6-2 a^7 z^5+20 a^5 z^5+53 a^3 z^5+64 a z^5+22 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +8 a^6 z^4-3 a^4 z^4-19 a^2 z^4+10 z^4 a^{-2} -5 z^4 a^{-4} +7 z^4+a^7 z^3-4 a^5 z^3-21 a^3 z^3-26 a z^3-6 z^3 a^{-1} +3 z^3 a^{-3} -z^3 a^{-5} +2 a^4 z^2+a^2 z^2-z^2 a^{-2} +z^2 a^{-4} -3 z^2+a^5 z+3 a^3 z+3 a z+z a^{-1} +1 }[/math] |
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