K12n787
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-3 q^6+6 q^5-9 q^4+11 q^3-12 q^2+11 q-8+6 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-9 t^2+14 t-15+14 t^{-1} -9 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-5 z^4-2 z^2+1 }[/math] |
| Determinant | 71 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +z^6-13 z^4 a^{-2} +4 z^4 a^{-4} +4 z^4-12 z^2 a^{-2} +5 z^2 a^{-4} +5 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +4 z^9 a^{-1} +5 z^9 a^{-3} +z^9 a^{-5} +4 z^8 a^{-2} -z^8 a^{-4} +5 z^8+3 a z^7-13 z^7 a^{-1} -17 z^7 a^{-3} -z^7 a^{-5} +a^2 z^6-24 z^6 a^{-2} +5 z^6 a^{-6} -18 z^6-9 a z^5+13 z^5 a^{-1} +24 z^5 a^{-3} +5 z^5 a^{-5} +3 z^5 a^{-7} -3 a^2 z^4+37 z^4 a^{-2} +7 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +19 z^4+4 a z^3-6 z^3 a^{-1} -11 z^3 a^{-3} -5 z^3 a^{-5} -4 z^3 a^{-7} +a^2 z^2-21 z^2 a^{-2} -7 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} -10 z^2+z a^{-1} +z a^{-3} +z a^{-5} +z a^{-7} +4 a^{-2} +2 a^{-4} +3 }[/math] |
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