K12n842
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-20 q^3+27 q^2-30 q+30-25 q^{-1} +18 q^{-2} -10 q^{-3} +3 q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+21 t^2-38 t+47-38 t^{-1} +21 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-z^4-z^2+1 }[/math] |
| Determinant | 181 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-2 z^6 a^{-2} +4 z^6-3 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +6 z^4+a^4 z^2-4 a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} +4 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{10} a^{-2} +5 z^{10}+13 a z^9+25 z^9 a^{-1} +12 z^9 a^{-3} +11 a^2 z^8+15 z^8 a^{-2} +11 z^8 a^{-4} +15 z^8+3 a^3 z^7-24 a z^7-51 z^7 a^{-1} -19 z^7 a^{-3} +5 z^7 a^{-5} -16 a^2 z^6-54 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -47 z^6+9 a^3 z^5+31 a z^5+32 z^5 a^{-1} +2 z^5 a^{-3} -8 z^5 a^{-5} +6 a^4 z^4+19 a^2 z^4+39 z^4 a^{-2} +13 z^4 a^{-4} -z^4 a^{-6} +38 z^4-12 a^3 z^3-24 a z^3-13 z^3 a^{-1} +2 z^3 a^{-3} +3 z^3 a^{-5} -5 a^4 z^2-12 a^2 z^2-9 z^2 a^{-2} -3 z^2 a^{-4} -13 z^2+3 a^3 z+6 a z+4 z a^{-1} +z a^{-3} +a^4+2 a^2+2 }[/math] |
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