K12n561
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+5 q^5-7 q^4+9 q^3-9 q^2+8 q-6+4 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^2+14 t-19+14 t^{-1} -4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^4-2 z^2+1 }[/math] |
| Determinant | 55 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^4 a^{-2} -z^4 a^{-4} -z^4+a^2 z^2-3 z^2 a^{-2} +z^2 a^{-6} -z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +2 z^9 a^{-1} +4 z^9 a^{-3} +2 z^9 a^{-5} -2 z^8 a^{-2} -3 z^8 a^{-4} +z^8 a^{-6} +2 z^8+2 a z^7-7 z^7 a^{-1} -19 z^7 a^{-3} -10 z^7 a^{-5} +a^2 z^6+4 z^6 a^{-4} -2 z^6 a^{-6} -5 z^6-7 a z^5+11 z^5 a^{-1} +39 z^5 a^{-3} +24 z^5 a^{-5} +3 z^5 a^{-7} -4 a^2 z^4+5 z^4 a^{-2} +3 z^4 a^{-4} +3 z^4 a^{-6} +z^4 a^{-8} +5 a z^3-12 z^3 a^{-1} -31 z^3 a^{-3} -20 z^3 a^{-5} -6 z^3 a^{-7} +4 a^2 z^2-6 z^2 a^{-2} -3 z^2 a^{-4} -z^2 a^{-6} -2 z^2 a^{-8} +2 z^2+4 z a^{-1} +8 z a^{-3} +6 z a^{-5} +2 z a^{-7} -a^2+ a^{-2} + a^{-4} }[/math] |
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