K12n529
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^7-6 q^6+11 q^5-16 q^4+19 q^3-19 q^2+17 q-13+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-10 t^2+28 t-37+28 t^{-1} -10 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-4 z^4-3 z^2+1 }[/math] |
| Determinant | 115 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^4 a^{-2} -3 z^4 a^{-4} -2 z^4+a^2 z^2-4 z^2 a^{-4} +2 z^2 a^{-6} -2 z^2+a^2- a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +4 z^9 a^{-1} +7 z^9 a^{-3} +3 z^9 a^{-5} +12 z^8 a^{-2} +10 z^8 a^{-4} +3 z^8 a^{-6} +5 z^8+3 a z^7-z^7 a^{-1} -2 z^7 a^{-3} +3 z^7 a^{-5} +z^7 a^{-7} +a^2 z^6-30 z^6 a^{-2} -18 z^6 a^{-4} +z^6 a^{-6} -10 z^6-7 a z^5-12 z^5 a^{-1} -18 z^5 a^{-3} -8 z^5 a^{-5} +5 z^5 a^{-7} -3 a^2 z^4+20 z^4 a^{-2} +7 z^4 a^{-4} -2 z^4 a^{-6} +3 z^4 a^{-8} +5 z^4+5 a z^3+8 z^3 a^{-1} +15 z^3 a^{-3} +6 z^3 a^{-5} -6 z^3 a^{-7} +3 a^2 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} +2 z^2 a^{-6} -3 z^2 a^{-8} -z^2-a z-2 z a^{-1} -3 z a^{-3} -z a^{-5} +z a^{-7} -a^2- a^{-4} - a^{-6} }[/math] |
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