K12a899
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-8 q^3+15 q^2-21 q+26-27 q^{-1} +26 q^{-2} -20 q^{-3} +14 q^{-4} -8 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+20 t^2-35 t+43-35 t^{-1} +20 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+12 z^4+5 z^2+1 }[/math] |
| Determinant | 173 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+5 a^2 z^6-z^6 a^{-2} +5 z^6-4 a^4 z^4+10 a^2 z^4-4 z^4 a^{-2} +10 z^4-6 a^4 z^2+9 a^2 z^2-6 z^2 a^{-2} +8 z^2-3 a^4+4 a^2-2 a^{-2} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+11 a^2 z^{10}+6 z^{10}+5 a^5 z^9+6 a^3 z^9+10 a z^9+9 z^9 a^{-1} +3 a^6 z^8-12 a^4 z^8-27 a^2 z^8+9 z^8 a^{-2} -3 z^8+a^7 z^7-15 a^5 z^7-30 a^3 z^7-34 a z^7-14 z^7 a^{-1} +6 z^7 a^{-3} -10 a^6 z^6+9 a^4 z^6+25 a^2 z^6-16 z^6 a^{-2} +3 z^6 a^{-4} -13 z^6-4 a^7 z^5+13 a^5 z^5+37 a^3 z^5+38 a z^5+9 z^5 a^{-1} -8 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4-11 a^4 z^4-18 a^2 z^4+17 z^4 a^{-2} -4 z^4 a^{-4} +23 z^4+5 a^7 z^3-6 a^5 z^3-26 a^3 z^3-20 a z^3+z^3 a^{-1} +4 z^3 a^{-3} -2 z^3 a^{-5} -2 a^6 z^2+10 a^4 z^2+11 a^2 z^2-10 z^2 a^{-2} +z^2 a^{-4} -12 z^2-2 a^7 z+2 a^5 z+8 a^3 z+4 a z-2 z a^{-1} -z a^{-3} +z a^{-5} -3 a^4-4 a^2+2 a^{-2} +2 }[/math] |
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