K12n818
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+7 q^5-11 q^4+14 q^3-15 q^2+14 q-12+8 q^{-1} -4 q^{-2} +2 q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-9 t^2+22 t-27+22 t^{-1} -9 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-3 z^4-5 z^2+1 }[/math] |
| Determinant | 91 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^4 a^{-2} -2 z^4 a^{-4} -3 z^4+2 a^2 z^2+2 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} -7 z^2+3 a^2+2 a^{-2} - a^{-4} + a^{-6} -4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+a z^9+5 z^9 a^{-1} +4 z^9 a^{-3} +6 z^8 a^{-2} +7 z^8 a^{-4} -z^8-a z^7-11 z^7 a^{-1} -2 z^7 a^{-3} +8 z^7 a^{-5} +3 a^2 z^6-14 z^6 a^{-2} -9 z^6 a^{-4} +6 z^6 a^{-6} +4 z^6-3 a z^5+9 z^5 a^{-1} -3 z^5 a^{-3} -12 z^5 a^{-5} +3 z^5 a^{-7} -11 a^2 z^4+3 z^4 a^{-2} +2 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} -18 z^4+3 a z^3-11 z^3 a^{-1} -3 z^3 a^{-3} +9 z^3 a^{-5} -2 z^3 a^{-7} +12 a^2 z^2+2 z^2 a^{-2} +3 z^2 a^{-4} +5 z^2 a^{-6} -z^2 a^{-8} +17 z^2+4 z a^{-1} +3 z a^{-3} -z a^{-5} -3 a^2-2 a^{-2} - a^{-4} - a^{-6} -4 }[/math] |
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