K12n706
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-4 q^3+6 q^2-8 q+9-8 q^{-1} +6 q^{-2} -4 q^{-3} +2 q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+6 t^2-8 t+11-8 t^{-1} +6 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+2 z^4-4 z^2+1 }[/math] |
| Determinant | 49 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +6 z^6-5 a^2 z^4-5 z^4 a^{-2} +12 z^4+a^4 z^2-8 a^2 z^2-8 z^2 a^{-2} +z^2 a^{-4} +10 z^2+2 a^4-4 a^2-4 a^{-2} +2 a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^9+2 z^9 a^{-1} +3 a^2 z^8+3 z^8 a^{-2} +6 z^8+a^3 z^7-7 a z^7-7 z^7 a^{-1} +z^7 a^{-3} -12 a^2 z^6-12 z^6 a^{-2} -24 z^6+a^3 z^5+13 a z^5+13 z^5 a^{-1} +z^5 a^{-3} +3 a^4 z^4+23 a^2 z^4+23 z^4 a^{-2} +3 z^4 a^{-4} +40 z^4-6 a^3 z^3-8 a z^3-8 z^3 a^{-1} -6 z^3 a^{-3} -7 a^4 z^2-18 a^2 z^2-18 z^2 a^{-2} -7 z^2 a^{-4} -22 z^2+2 a^3 z+2 a z+2 z a^{-1} +2 z a^{-3} +2 a^4+4 a^2+4 a^{-2} +2 a^{-4} +5 }[/math] |
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