K12n670
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+q^3-q^2+3-3 q^{-1} +5 q^{-2} -5 q^{-3} +5 q^{-4} -4 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-2 t^3+3 t^2-4 t+5-4 t^{-1} +3 t^{-2} -2 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+6 z^6+11 z^4+6 z^2+1 }[/math] |
| Determinant | 25 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8-a^4 z^6+7 a^2 z^6-5 a^4 z^4+17 a^2 z^4-z^4 a^{-2} -8 a^4 z^2+17 a^2 z^2-3 z^2 a^{-2} -4 a^4+6 a^2-2 a^{-2} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+2 a^5 z^9+3 a^3 z^9+a z^9+2 a^6 z^8-3 a^4 z^8-6 a^2 z^8+z^8 a^{-2} +a^7 z^7-8 a^5 z^7-16 a^3 z^7-7 a z^7+z^7 a^{-1} +z^7 a^{-3} -9 a^6 z^6+13 a^2 z^6-6 z^6 a^{-2} -2 z^6-5 a^7 z^5+6 a^5 z^5+27 a^3 z^5+13 a z^5-9 z^5 a^{-1} -6 z^5 a^{-3} +10 a^6 z^4-3 a^4 z^4-19 a^2 z^4+9 z^4 a^{-2} +3 z^4+7 a^7 z^3-a^5 z^3-23 a^3 z^3-9 a z^3+16 z^3 a^{-1} +10 z^3 a^{-3} -3 a^6 z^2+8 a^4 z^2+16 a^2 z^2-5 z^2 a^{-2} -3 a^7 z+a^5 z+8 a^3 z+2 a z-7 z a^{-1} -5 z a^{-3} -4 a^4-6 a^2+2 a^{-2} +1 }[/math] |
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