K12a544
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-7 q^5+12 q^4-18 q^3+23 q^2-24 q+24-19 q^{-1} +14 q^{-2} -8 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+19 t^2-31 t+37-31 t^{-1} +19 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+11 z^4+5 z^2+1 }[/math] |
| Determinant | 157 |
| 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} +10 z^4-6 a^2 z^2+6 z^2 a^{-2} -5 z^2 a^{-4} +10 z^2-3 a^2+ a^{-2} -2 a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +7 z^{10} a^{-2} +3 z^{10} a^{-4} +4 z^{10}+7 a z^9+11 z^9 a^{-1} +8 z^9 a^{-3} +4 z^9 a^{-5} +8 a^2 z^8-10 z^8 a^{-2} -2 z^8 a^{-4} +3 z^8 a^{-6} +3 z^8+6 a^3 z^7-7 a z^7-28 z^7 a^{-1} -27 z^7 a^{-3} -11 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-13 a^2 z^6-2 z^6 a^{-2} -12 z^6 a^{-4} -11 z^6 a^{-6} -17 z^6+a^5 z^5-9 a^3 z^5-a z^5+24 z^5 a^{-1} +25 z^5 a^{-3} +6 z^5 a^{-5} -4 z^5 a^{-7} -4 a^4 z^4+13 a^2 z^4+3 z^4 a^{-2} +11 z^4 a^{-4} +12 z^4 a^{-6} +21 z^4-2 a^5 z^3+6 a^3 z^3+8 a z^3-8 z^3 a^{-1} -12 z^3 a^{-3} +z^3 a^{-5} +5 z^3 a^{-7} +a^4 z^2-9 a^2 z^2+z^2 a^{-2} +z^2 a^{-4} -4 z^2 a^{-6} -14 z^2+a^5 z-2 a^3 z-5 a z-z a^{-1} +3 z a^{-3} -2 z a^{-7} +3 a^2- a^{-2} -2 a^{-4} +5 }[/math] |
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