K12a1174
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-7 q^5+12 q^4-17 q^3+21 q^2-22 q+22-17 q^{-1} +12 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+18 t^2-28 t+33-28 t^{-1} +18 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+10 z^4+4 z^2+1 }[/math] |
| Determinant | 145 |
| 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+9 z^4 a^{-2} -4 z^4 a^{-4} +9 z^4-5 a^2 z^2+7 z^2 a^{-2} -5 z^2 a^{-4} +7 z^2-2 a^2+2 a^{-2} -2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +10 z^{10} a^{-2} +5 z^{10} a^{-4} +5 z^{10}+7 a z^9+4 z^9 a^{-1} +2 z^9 a^{-3} +5 z^9 a^{-5} +7 a^2 z^8-35 z^8 a^{-2} -18 z^8 a^{-4} +3 z^8 a^{-6} -7 z^8+5 a^3 z^7-14 a z^7-24 z^7 a^{-1} -25 z^7 a^{-3} -19 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-14 a^2 z^6+50 z^6 a^{-2} +27 z^6 a^{-4} -11 z^6 a^{-6} -5 z^6+a^5 z^5-7 a^3 z^5+10 a z^5+34 z^5 a^{-1} +45 z^5 a^{-3} +25 z^5 a^{-5} -4 z^5 a^{-7} -5 a^4 z^4+14 a^2 z^4-36 z^4 a^{-2} -28 z^4 a^{-4} +10 z^4 a^{-6} +21 z^4-2 a^5 z^3+a^3 z^3+4 a z^3-15 z^3 a^{-1} -39 z^3 a^{-3} -19 z^3 a^{-5} +4 z^3 a^{-7} +a^4 z^2-9 a^2 z^2+12 z^2 a^{-2} +11 z^2 a^{-4} -z^2 a^{-6} -10 z^2+a^5 z-a^3 z-3 a z+3 z a^{-1} +10 z a^{-3} +6 z a^{-5} +2 a^2-2 a^{-2} -2 a^{-4} +3 }[/math] |
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