K12n486
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-5 q^2+7 q-8+9 q^{-1} -8 q^{-2} +7 q^{-3} -4 q^{-4} +2 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-7 t^2+12 t-13+12 t^{-1} -7 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+5 z^4+2 z^2+1 }[/math] |
| Determinant | 55 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6+z^6-a^4 z^4+4 a^2 z^4-z^4 a^{-2} +3 z^4-3 a^4 z^2+6 a^2 z^2-2 z^2 a^{-2} +z^2-2 a^4+4 a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+a^3 z^9+4 a z^9+3 z^9 a^{-1} -3 a^2 z^8+3 z^8 a^{-2} -2 a^3 z^7-15 a z^7-12 z^7 a^{-1} +z^7 a^{-3} +5 a^4 z^6+9 a^2 z^6-13 z^6 a^{-2} -9 z^6+3 a^5 z^5+6 a^3 z^5+20 a z^5+13 z^5 a^{-1} -4 z^5 a^{-3} +2 a^6 z^4-10 a^4 z^4-20 a^2 z^4+15 z^4 a^{-2} +7 z^4+a^7 z^3-2 a^5 z^3-10 a^3 z^3-17 a z^3-6 z^3 a^{-1} +4 z^3 a^{-3} -a^6 z^2+9 a^4 z^2+15 a^2 z^2-4 z^2 a^{-2} +z^2-a^7 z+a^5 z+5 a^3 z+5 a z+2 z a^{-1} -2 a^4-4 a^2-1 }[/math] |
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