K12n708
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+2 q^6-4 q^5+6 q^4-7 q^3+8 q^2-7 q+7-4 q^{-1} +2 q^{-2} - q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-3 t^3+6 t^2-9 t+11-9 t^{-1} +6 t^{-2} -3 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+5 z^6+8 z^4+4 z^2+1 }[/math] |
| Determinant | 49 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +7 z^6 a^{-2} -z^6 a^{-4} -z^6+18 z^4 a^{-2} -5 z^4 a^{-4} -5 z^4+20 z^2 a^{-2} -8 z^2 a^{-4} -8 z^2+8 a^{-2} -4 a^{-4} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +3 z^9 a^{-3} +2 z^9 a^{-5} -5 z^8 a^{-2} -3 z^8 a^{-4} +2 z^8 a^{-6} -3 z^7 a^{-1} -12 z^7 a^{-3} -8 z^7 a^{-5} +z^7 a^{-7} +19 z^6 a^{-2} +5 z^6 a^{-4} -9 z^6 a^{-6} +5 z^6+3 a z^5+10 z^5 a^{-1} +21 z^5 a^{-3} +9 z^5 a^{-5} -5 z^5 a^{-7} +2 a^2 z^4-37 z^4 a^{-2} -13 z^4 a^{-4} +11 z^4 a^{-6} -11 z^4+a^3 z^3-2 a z^3-15 z^3 a^{-1} -24 z^3 a^{-3} -5 z^3 a^{-5} +7 z^3 a^{-7} -a^2 z^2+28 z^2 a^{-2} +12 z^2 a^{-4} -3 z^2 a^{-6} +12 z^2-a^3 z+a z+7 z a^{-1} +9 z a^{-3} +2 z a^{-5} -2 z a^{-7} -8 a^{-2} -4 a^{-4} -3 }[/math] |
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