K12n658
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^9+4 q^8-8 q^7+11 q^6-14 q^5+15 q^4-13 q^3+11 q^2-7 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+12 t^2-17 t+19-17 t^{-1} +12 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -3 z^4 a^{-2} +8 z^4 a^{-4} -3 z^4 a^{-6} -z^2 a^{-2} +5 z^2 a^{-4} -2 z^2 a^{-6} + a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-3} +9 z^9 a^{-5} +4 z^9 a^{-7} +4 z^8 a^{-2} +2 z^8 a^{-4} +z^8 a^{-6} +3 z^8 a^{-8} +z^7 a^{-1} -17 z^7 a^{-3} -28 z^7 a^{-5} -9 z^7 a^{-7} +z^7 a^{-9} -15 z^6 a^{-2} -25 z^6 a^{-4} -13 z^6 a^{-6} -3 z^6 a^{-8} -3 z^5 a^{-1} +13 z^5 a^{-3} +23 z^5 a^{-5} +11 z^5 a^{-7} +4 z^5 a^{-9} +15 z^4 a^{-2} +27 z^4 a^{-4} +11 z^4 a^{-6} +3 z^4 a^{-8} +4 z^4 a^{-10} +2 z^3 a^{-1} -z^3 a^{-3} -8 z^3 a^{-5} -9 z^3 a^{-7} -3 z^3 a^{-9} +z^3 a^{-11} -3 z^2 a^{-2} -8 z^2 a^{-4} -5 z^2 a^{-6} -z^2 a^{-8} -z^2 a^{-10} +z a^{-3} +z a^{-5} +z a^{-7} +z a^{-9} - a^{-2} + a^{-4} + a^{-6} }[/math] |
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