K12a211
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-8 q^5+14 q^4-20 q^3+25 q^2-26 q+26-20 q^{-1} +14 q^{-2} -8 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+20 t^2-34 t+41-34 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+6 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+5 z^6 a^{-2} -z^6 a^{-4} +5 z^6-4 a^2 z^4+10 z^4 a^{-2} -4 z^4 a^{-4} +10 z^4-6 a^2 z^2+9 z^2 a^{-2} -6 z^2 a^{-4} +9 z^2-3 a^2+3 a^{-2} -3 a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +4 z^{10} a^{-4} +4 z^{10}+7 a z^9+14 z^9 a^{-1} +12 z^9 a^{-3} +5 z^9 a^{-5} +8 a^2 z^8-9 z^8 a^{-2} -5 z^8 a^{-4} +3 z^8 a^{-6} +7 z^8+6 a^3 z^7-4 a z^7-35 z^7 a^{-1} -41 z^7 a^{-3} -15 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-12 a^2 z^6-9 z^6 a^{-2} -7 z^6 a^{-4} -10 z^6 a^{-6} -27 z^6+a^5 z^5-9 a^3 z^5-8 a z^5+29 z^5 a^{-1} +45 z^5 a^{-3} +14 z^5 a^{-5} -4 z^5 a^{-7} -4 a^4 z^4+12 a^2 z^4+6 z^4 a^{-2} +5 z^4 a^{-4} +10 z^4 a^{-6} +27 z^4-2 a^5 z^3+7 a^3 z^3+14 a z^3-12 z^3 a^{-1} -29 z^3 a^{-3} -7 z^3 a^{-5} +5 z^3 a^{-7} +a^4 z^2-8 a^2 z^2+4 z^2 a^{-2} +4 z^2 a^{-4} -3 z^2 a^{-6} -12 z^2+a^5 z-3 a^3 z-6 a z+2 z a^{-1} +9 z a^{-3} +3 z a^{-5} -2 z a^{-7} +3 a^2-3 a^{-2} -3 a^{-4} +4 }[/math] |
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