K12n541
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-7+11 q^{-1} -13 q^{-2} +14 q^{-3} -13 q^{-4} +10 q^{-5} -6 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-9 t^2+19 t-23+19 t^{-1} -9 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 83 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+3 z^4 a^4+4 z^2 a^4+2 a^4+z^6 a^2+2 z^4 a^2-a^2-z^4-z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+4 a^5 z^9+5 a^3 z^9+a z^9+6 a^6 z^8+5 a^4 z^8-a^2 z^8+5 a^7 z^7-8 a^5 z^7-14 a^3 z^7-a z^7+3 a^8 z^6-16 a^6 z^6-19 a^4 z^6+4 a^2 z^6+4 z^6+a^9 z^5-11 a^7 z^5+6 a^5 z^5+22 a^3 z^5+5 a z^5+z^5 a^{-1} -6 a^8 z^4+18 a^6 z^4+28 a^4 z^4-4 a^2 z^4-8 z^4-2 a^9 z^3+7 a^7 z^3+4 a^5 z^3-14 a^3 z^3-11 a z^3-2 z^3 a^{-1} +a^8 z^2-7 a^6 z^2-13 a^4 z^2-3 a^2 z^2+2 z^2-2 a^7 z-2 a^5 z+2 a^3 z+3 a z+z a^{-1} +a^6+2 a^4+a^2+1 }[/math] |
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