K12a465
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+11 q^4-20 q^3+29 q^2-36 q+39-36 q^{-1} +29 q^{-2} -20 q^{-3} +11 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+26 t^2-52 t+67-52 t^{-1} +26 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^4-4 z^2+1 }[/math] |
| Determinant | 241 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-6 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +8 z^4+2 a^4 z^2-8 a^2 z^2-8 z^2 a^{-2} +2 z^2 a^{-4} +8 z^2+2 a^4-4 a^2-4 a^{-2} +2 a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +7 a^2 z^{10}+7 z^{10} a^{-2} +14 z^{10}+11 a^3 z^9+23 a z^9+23 z^9 a^{-1} +11 z^9 a^{-3} +9 a^4 z^8+9 a^2 z^8+9 z^8 a^{-2} +9 z^8 a^{-4} +4 a^5 z^7-16 a^3 z^7-48 a z^7-48 z^7 a^{-1} -16 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-18 a^4 z^6-46 a^2 z^6-46 z^6 a^{-2} -18 z^6 a^{-4} +z^6 a^{-6} -54 z^6-7 a^5 z^5+5 a^3 z^5+22 a z^5+22 z^5 a^{-1} +5 z^5 a^{-3} -7 z^5 a^{-5} -2 a^6 z^4+16 a^4 z^4+49 a^2 z^4+49 z^4 a^{-2} +16 z^4 a^{-4} -2 z^4 a^{-6} +62 z^4+4 a^5 z^3+a^3 z^3+3 a z^3+3 z^3 a^{-1} +z^3 a^{-3} +4 z^3 a^{-5} +a^6 z^2-9 a^4 z^2-23 a^2 z^2-23 z^2 a^{-2} -9 z^2 a^{-4} +z^2 a^{-6} -26 z^2-a^5 z-a^3 z-2 a z-2 z a^{-1} -z a^{-3} -z a^{-5} +2 a^4+4 a^2+4 a^{-2} +2 a^{-4} +5 }[/math] |
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