K12a894
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-13 q^5+23 q^4-33 q^3+41 q^2-43 q+41-33 q^{-1} +22 q^{-2} -12 q^{-3} +5 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+33 t^2-56 t+67-56 t^{-1} +33 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+4 z^6+z^4+1 }[/math] |
| Determinant | 273 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+3 z^6 a^{-2} -z^6 a^{-4} +3 z^6-2 a^2 z^4+3 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4+3 z^2 a^{-2} -z^2 a^{-4} -2 z^2+a^2+3 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{11} a^{-1} +5 z^{11} a^{-3} +27 z^{10} a^{-2} +12 z^{10} a^{-4} +15 z^{10}+21 a z^9+25 z^9 a^{-1} +15 z^9 a^{-3} +11 z^9 a^{-5} +19 a^2 z^8-58 z^8 a^{-2} -25 z^8 a^{-4} +5 z^8 a^{-6} -9 z^8+12 a^3 z^7-29 a z^7-77 z^7 a^{-1} -66 z^7 a^{-3} -29 z^7 a^{-5} +z^7 a^{-7} +5 a^4 z^6-25 a^2 z^6+28 z^6 a^{-2} +9 z^6 a^{-4} -12 z^6 a^{-6} -23 z^6+a^5 z^5-12 a^3 z^5+8 a z^5+54 z^5 a^{-1} +58 z^5 a^{-3} +23 z^5 a^{-5} -2 z^5 a^{-7} -3 a^4 z^4+10 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} +8 z^4 a^{-6} +18 z^4+3 a^3 z^3+4 a z^3-7 z^3 a^{-1} -16 z^3 a^{-3} -7 z^3 a^{-5} +z^3 a^{-7} +4 z^2 a^{-2} +z^2 a^{-4} -z^2 a^{-6} +2 z^2-a z-z a^{-1} +z a^{-3} +z a^{-5} -a^2-3 a^{-2} - a^{-4} -2 }[/math] |
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