K12a188
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-12 q^3+21 q^2-29 q+34-35 q^{-1} +32 q^{-2} -24 q^{-3} +16 q^{-4} -8 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+26 t^2-47 t+57-47 t^{-1} +26 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^4+z^2+1 }[/math] |
| Determinant | 221 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-10 a^2 z^4-2 z^4 a^{-2} +7 z^4-a^6 z^2+8 a^4 z^2-11 a^2 z^2-z^2 a^{-2} +6 z^2-2 a^6+5 a^4-4 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+14 a^2 z^{10}+9 z^{10}+5 a^5 z^9+13 a^3 z^9+25 a z^9+17 z^9 a^{-1} +3 a^6 z^8-6 a^4 z^8-20 a^2 z^8+18 z^8 a^{-2} +7 z^8+a^7 z^7-13 a^5 z^7-48 a^3 z^7-68 a z^7-22 z^7 a^{-1} +12 z^7 a^{-3} -10 a^6 z^6-11 a^4 z^6-14 a^2 z^6-26 z^6 a^{-2} +5 z^6 a^{-4} -44 z^6-4 a^7 z^5+9 a^5 z^5+53 a^3 z^5+58 a z^5+4 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+23 a^4 z^4+36 a^2 z^4+11 z^4 a^{-2} -3 z^4 a^{-4} +38 z^4+5 a^7 z^3-a^5 z^3-24 a^3 z^3-20 a z^3+z^3 a^{-1} +3 z^3 a^{-3} -6 a^6 z^2-17 a^4 z^2-21 a^2 z^2-2 z^2 a^{-2} -12 z^2-2 a^7 z-a^5 z+3 a^3 z+2 a z+2 a^6+5 a^4+4 a^2+2 }[/math] |
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