K12n847
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^6+6 q^5-9 q^4+12 q^3-13 q^2+12 q-10+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-7 t^2+18 t-23+18 t^{-1} -7 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-z^4-z^2+1 }[/math] |
| Determinant | 75 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^4 a^{-2} -z^4 a^{-4} -2 z^4+a^2 z^2+z^2 a^{-4} -3 z^2+a^2-2 a^{-2} +3 a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +3 z^9 a^{-1} +4 z^9 a^{-3} +z^9 a^{-5} +2 z^8 a^{-2} -2 z^8 a^{-4} +4 z^8+3 a z^7-4 z^7 a^{-1} -10 z^7 a^{-3} -3 z^7 a^{-5} +a^2 z^6-4 z^6 a^{-2} +6 z^6 a^{-4} +z^6 a^{-6} -8 z^6-8 a z^5-z^5 a^{-1} +19 z^5 a^{-3} +12 z^5 a^{-5} -3 a^2 z^4-z^4 a^{-2} +2 z^4 a^{-4} +5 z^4 a^{-6} -z^4+5 a z^3-5 z^3 a^{-1} -21 z^3 a^{-3} -9 z^3 a^{-5} +2 z^3 a^{-7} +3 a^2 z^2-4 z^2 a^{-2} -9 z^2 a^{-4} -4 z^2 a^{-6} +4 z^2+4 z a^{-1} +7 z a^{-3} +3 z a^{-5} -a^2+2 a^{-2} +3 a^{-4} + a^{-6} }[/math] |
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