K12n483
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+q^4-q^2+3 q-3+4 q^{-1} -4 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^2+4 t-5+4 t^{-1} - t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-z^4 }[/math] |
| Determinant | 15 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} +z^6-a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +5 z^4-2 a^2 z^2-9 z^2 a^{-2} +3 z^2 a^{-4} +8 z^2-a^2-3 a^{-2} + a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+3 a z^9+4 z^9 a^{-1} +z^9 a^{-3} +3 a^2 z^8-3 z^8 a^{-2} +z^8 a^{-4} -z^8+a^3 z^7-14 a z^7-22 z^7 a^{-1} -5 z^7 a^{-3} +2 z^7 a^{-5} -14 a^2 z^6-11 z^6 a^{-2} -6 z^6 a^{-4} +z^6 a^{-6} -18 z^6-4 a^3 z^5+12 a z^5+25 z^5 a^{-1} -z^5 a^{-3} -10 z^5 a^{-5} +15 a^2 z^4+30 z^4 a^{-2} +6 z^4 a^{-4} -4 z^4 a^{-6} +35 z^4+3 a^3 z^3+2 a z^3+z^3 a^{-1} +11 z^3 a^{-3} +9 z^3 a^{-5} -6 a^2 z^2-19 z^2 a^{-2} -4 z^2 a^{-4} +2 z^2 a^{-6} -19 z^2-a^3 z-3 a z-5 z a^{-1} -5 z a^{-3} -2 z a^{-5} +a^2+3 a^{-2} + a^{-4} +4 }[/math] |
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