K12a765
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-24 q^3+35 q^2-42 q+45-41 q^{-1} +33 q^{-2} -22 q^{-3} +11 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+31 t^2-60 t+75-60 t^{-1} +31 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-3 z^4-z^2+1 }[/math] |
| Determinant | 277 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-5 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +4 z^4+2 a^4 z^2-5 a^2 z^2-2 z^2 a^{-2} +z^2 a^{-4} +3 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +10 a^2 z^{10}+11 z^{10} a^{-2} +21 z^{10}+13 a^3 z^9+30 a z^9+33 z^9 a^{-1} +16 z^9 a^{-3} +9 a^4 z^8+a^2 z^8+5 z^8 a^{-2} +12 z^8 a^{-4} -15 z^8+4 a^5 z^7-22 a^3 z^7-77 a z^7-81 z^7 a^{-1} -25 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-16 a^4 z^6-33 a^2 z^6-46 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -40 z^6-7 a^5 z^5+17 a^3 z^5+65 a z^5+59 z^5 a^{-1} +11 z^5 a^{-3} -7 z^5 a^{-5} -2 a^6 z^4+13 a^4 z^4+38 a^2 z^4+38 z^4 a^{-2} +14 z^4 a^{-4} -z^4 a^{-6} +46 z^4+4 a^5 z^3-6 a^3 z^3-24 a z^3-20 z^3 a^{-1} -3 z^3 a^{-3} +3 z^3 a^{-5} +a^6 z^2-6 a^4 z^2-16 a^2 z^2-10 z^2 a^{-2} -4 z^2 a^{-4} -15 z^2-a^5 z+3 a z+3 z a^{-1} +z a^{-3} +a^4+2 a^2+2 }[/math] |
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