K12n580
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+3 q^2-6 q+9-10 q^{-1} +11 q^{-2} -9 q^{-3} +8 q^{-4} -5 q^{-5} +2 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^2-16 t+23-16 t^{-1} +5 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^4+4 z^2+1 }[/math] |
| Determinant | 65 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+z^4 a^4-a^4+3 z^4 a^2+7 z^2 a^2+5 a^2+z^4-z^2-2-z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+2 a^5 z^9+4 a^3 z^9+2 a z^9+2 a^6 z^8-a^2 z^8+z^8+a^7 z^7-5 a^5 z^7-11 a^3 z^7-5 a z^7-8 a^6 z^6-5 a^4 z^6+6 a^2 z^6+3 z^6-5 a^7 z^5-2 a^5 z^5+10 a^3 z^5+13 a z^5+6 z^5 a^{-1} +9 a^6 z^4-3 a^4 z^4-21 a^2 z^4+3 z^4 a^{-2} -6 z^4+8 a^7 z^3+8 a^5 z^3-11 a^3 z^3-18 a z^3-6 z^3 a^{-1} +z^3 a^{-3} -3 a^6 z^2+7 a^4 z^2+17 a^2 z^2-z^2 a^{-2} +6 z^2-4 a^7 z-3 a^5 z+5 a^3 z+7 a z+3 z a^{-1} +a^6-a^4-5 a^2-2 }[/math] |
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