K12n664
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 3 q^4-9 q^3+16 q^2-23 q+27-27 q^{-1} +25 q^{-2} -18 q^{-3} +11 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+20 t^2-34 t+41-34 t^{-1} +20 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-2 z^4-z^2+1 }[/math] |
| Determinant | 165 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-z^6 a^{-2} +4 z^6+a^4 z^4-5 a^2 z^4-3 z^4 a^{-2} +5 z^4+a^4 z^2-a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} +z^2-a^4+3 a^2- a^{-2} + a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^2 z^{10}+3 z^{10}+9 a^3 z^9+18 a z^9+9 z^9 a^{-1} +10 a^4 z^8+20 a^2 z^8+9 z^8 a^{-2} +19 z^8+5 a^5 z^7-8 a^3 z^7-25 a z^7-9 z^7 a^{-1} +3 z^7 a^{-3} +a^6 z^6-21 a^4 z^6-59 a^2 z^6-13 z^6 a^{-2} -50 z^6-9 a^5 z^5-15 a^3 z^5-6 a z^5+6 z^5 a^{-1} +6 z^5 a^{-3} -a^6 z^4+13 a^4 z^4+41 a^2 z^4+18 z^4 a^{-2} +6 z^4 a^{-4} +39 z^4+4 a^5 z^3+13 a^3 z^3+11 a z^3-7 z^3 a^{-1} -9 z^3 a^{-3} -2 a^4 z^2-6 a^2 z^2-12 z^2 a^{-2} -6 z^2 a^{-4} -10 z^2-a^3 z+4 z a^{-1} +3 z a^{-3} -a^4-3 a^2+ a^{-2} + a^{-4} -1 }[/math] |
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