K12a448
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+6 q^6-9 q^5+13 q^4-15 q^3+15 q^2-15 q+12-8 q^{-1} +5 q^{-2} -2 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^2-26 t+43-26 t^{-1} +5 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^4-6 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4-2 z^2 a^2+z^4-2 z^2+2 z^4 a^{-2} -z^2 a^{-2} -2 a^{-2} +2 z^4 a^{-4} +2 z^2 a^{-4} +3 a^{-4} -3 z^2 a^{-6} -2 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +5 z^9 a^{-1} +6 z^9 a^{-3} +4 z^9 a^{-5} +3 z^9 a^{-7} -2 z^8 a^{-2} -19 z^8 a^{-4} -11 z^8 a^{-6} +z^8 a^{-8} +5 z^8+4 a z^7-12 z^7 a^{-1} -33 z^7 a^{-3} -32 z^7 a^{-5} -15 z^7 a^{-7} +3 a^2 z^6-16 z^6 a^{-2} +6 z^6 a^{-4} +5 z^6 a^{-6} -5 z^6 a^{-8} -9 z^6+2 a^3 z^5-4 a z^5+13 z^5 a^{-1} +44 z^5 a^{-3} +48 z^5 a^{-5} +23 z^5 a^{-7} +a^4 z^4-2 a^2 z^4+24 z^4 a^{-2} +18 z^4 a^{-4} +12 z^4 a^{-6} +8 z^4 a^{-8} +7 z^4-2 a^3 z^3+2 a z^3-12 z^3 a^{-1} -28 z^3 a^{-3} -24 z^3 a^{-5} -12 z^3 a^{-7} -2 a^4 z^2-14 z^2 a^{-2} -16 z^2 a^{-4} -10 z^2 a^{-6} -5 z^2 a^{-8} -z^2+6 z a^{-1} +8 z a^{-3} +4 z a^{-5} +2 z a^{-7} +a^4+2 a^{-2} +3 a^{-4} +2 a^{-6} + a^{-8} }[/math] |
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