K12a141
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-7 q^5+13 q^4-18 q^3+23 q^2-25 q+24-20 q^{-1} +14 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+20 t^2-33 t+39-33 t^{-1} +20 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-2 z^4+1 }[/math] |
| Determinant | 161 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +5 z^6-3 a^2 z^4-12 z^4 a^{-2} +3 z^4 a^{-4} +10 z^4-2 a^2 z^2-15 z^2 a^{-2} +9 z^2 a^{-4} -z^2 a^{-6} +9 z^2-6 a^{-2} +6 a^{-4} -2 a^{-6} +3 }[/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+12 z^9 a^{-1} +9 z^9 a^{-3} +4 z^9 a^{-5} +8 a^2 z^8-6 z^8 a^{-2} +3 z^8 a^{-6} +5 z^8+7 a^3 z^7-4 a z^7-30 z^7 a^{-1} -30 z^7 a^{-3} -10 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-8 a^2 z^6-23 z^6 a^{-2} -23 z^6 a^{-4} -11 z^6 a^{-6} -23 z^6+a^5 z^5-10 a^3 z^5-9 a z^5+20 z^5 a^{-1} +24 z^5 a^{-3} +2 z^5 a^{-5} -4 z^5 a^{-7} -6 a^4 z^4-2 a^2 z^4+41 z^4 a^{-2} +34 z^4 a^{-4} +13 z^4 a^{-6} +24 z^4-a^5 z^3+4 a^3 z^3+12 a z^3+2 z^3 a^{-1} -4 z^3 a^{-3} +6 z^3 a^{-5} +5 z^3 a^{-7} +2 a^4 z^2+3 a^2 z^2-26 z^2 a^{-2} -22 z^2 a^{-4} -7 z^2 a^{-6} -10 z^2-a^3 z-4 a z-4 z a^{-1} -2 z a^{-3} -3 z a^{-5} -2 z a^{-7} +6 a^{-2} +6 a^{-4} +2 a^{-6} +3 }[/math] |
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