K12n618
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+5 q^5-10 q^4+14 q^3-17 q^2+18 q-16+13 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-15 t^2+21 t-21+21 t^{-1} -15 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+z^4-z^2+1 }[/math] |
| Determinant | 107 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-9 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-8 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +6 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+5 a z^9+11 z^9 a^{-1} +6 z^9 a^{-3} +4 a^2 z^8+9 z^8 a^{-2} +6 z^8 a^{-4} +7 z^8+a^3 z^7-13 a z^7-27 z^7 a^{-1} -11 z^7 a^{-3} +2 z^7 a^{-5} -14 a^2 z^6-38 z^6 a^{-2} -12 z^6 a^{-4} -40 z^6-3 a^3 z^5+2 a z^5+7 z^5 a^{-1} +5 z^5 a^{-3} +3 z^5 a^{-5} +15 a^2 z^4+36 z^4 a^{-2} +15 z^4 a^{-4} +5 z^4 a^{-6} +41 z^4+3 a^3 z^3+9 a z^3+8 z^3 a^{-1} +z^3 a^{-3} +z^3 a^{-7} -5 a^2 z^2-15 z^2 a^{-2} -7 z^2 a^{-4} -z^2 a^{-6} -14 z^2-a^3 z-3 a z-3 z a^{-1} -2 z a^{-3} -z a^{-5} +2 a^{-2} + a^{-4} +2 }[/math] |
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