K12a617
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-10 q^5+16 q^4-22 q^3+27 q^2-27 q+26-20 q^{-1} +13 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+22 t^2-35 t+41-35 t^{-1} +22 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+8 z^4+4 z^2+1 }[/math] |
| Determinant | 177 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +5 z^6-4 a^2 z^4+5 z^4 a^{-2} -3 z^4 a^{-4} +10 z^4-5 a^2 z^2+3 z^2 a^{-2} -3 z^2 a^{-4} +9 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} +12 z^{10} a^{-2} +6 z^{10} a^{-4} +6 z^{10}+8 a z^9+12 z^9 a^{-1} +11 z^9 a^{-3} +7 z^9 a^{-5} +7 a^2 z^8-26 z^8 a^{-2} -10 z^8 a^{-4} +4 z^8 a^{-6} -5 z^8+5 a^3 z^7-14 a z^7-45 z^7 a^{-1} -47 z^7 a^{-3} -20 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-10 a^2 z^6+5 z^6 a^{-2} -9 z^6 a^{-4} -12 z^6 a^{-6} -11 z^6+a^5 z^5-6 a^3 z^5+13 a z^5+50 z^5 a^{-1} +47 z^5 a^{-3} +14 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4+8 a^2 z^4+15 z^4 a^{-2} +12 z^4 a^{-4} +10 z^4 a^{-6} +26 z^4-2 a^5 z^3+a^3 z^3-3 a z^3-18 z^3 a^{-1} -20 z^3 a^{-3} -5 z^3 a^{-5} +3 z^3 a^{-7} +2 a^4 z^2-6 a^2 z^2-5 z^2 a^{-2} -z^2 a^{-4} -3 z^2 a^{-6} -15 z^2+a^5 z-a z+2 z a^{-1} +5 z a^{-3} +2 z a^{-5} -z a^{-7} +2 a^2-2 a^{-2} -2 a^{-4} +3 }[/math] |
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