K12a993
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-9 q^5+16 q^4-23 q^3+28 q^2-30 q+29-23 q^{-1} +16 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+24 t^2-38 t+45-38 t^{-1} +24 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+4 z^4+1 }[/math] |
| Determinant | 193 |
| 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} +4 z^6-3 a^2 z^4+5 z^4 a^{-2} -3 z^4 a^{-4} +5 z^4-2 a^2 z^2+2 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +16 z^{10} a^{-2} +7 z^{10} a^{-4} +9 z^{10}+13 a z^9+12 z^9 a^{-1} +6 z^9 a^{-3} +7 z^9 a^{-5} +12 a^2 z^8-47 z^8 a^{-2} -18 z^8 a^{-4} +4 z^8 a^{-6} -13 z^8+8 a^3 z^7-29 a z^7-55 z^7 a^{-1} -41 z^7 a^{-3} -22 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-23 a^2 z^6+47 z^6 a^{-2} +11 z^6 a^{-4} -13 z^6 a^{-6} -4 z^6+a^5 z^5-11 a^3 z^5+29 a z^5+72 z^5 a^{-1} +54 z^5 a^{-3} +20 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4+18 a^2 z^4-17 z^4 a^{-2} -4 z^4 a^{-4} +11 z^4 a^{-6} +21 z^4-a^5 z^3+2 a^3 z^3-11 a z^3-35 z^3 a^{-1} -32 z^3 a^{-3} -9 z^3 a^{-5} +2 z^3 a^{-7} -6 a^2 z^2-2 z^2 a^{-6} -8 z^2+2 a z+6 z a^{-1} +6 z a^{-3} +2 z a^{-5} +1 }[/math] |
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