K12n283
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+4 q^5-7 q^4+11 q^3-14 q^2+14 q-13+11 q^{-1} -7 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-14 t^2+16 t-13+16 t^{-1} -14 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+2 z^4-2 z^2+1 }[/math] |
| Determinant | 87 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-8 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +4 z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+5 a z^9+10 z^9 a^{-1} +5 z^9 a^{-3} +4 a^2 z^8+3 z^8 a^{-2} +4 z^8 a^{-4} +3 z^8+a^3 z^7-17 a z^7-35 z^7 a^{-1} -16 z^7 a^{-3} +z^7 a^{-5} -15 a^2 z^6-28 z^6 a^{-2} -11 z^6 a^{-4} -32 z^6-3 a^3 z^5+13 a z^5+35 z^5 a^{-1} +22 z^5 a^{-3} +3 z^5 a^{-5} +15 a^2 z^4+37 z^4 a^{-2} +18 z^4 a^{-4} +4 z^4 a^{-6} +38 z^4+2 a^3 z^3-3 a z^3-16 z^3 a^{-1} -15 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} -4 a^2 z^2-16 z^2 a^{-2} -11 z^2 a^{-4} -3 z^2 a^{-6} -12 z^2+a z+5 z a^{-1} +5 z a^{-3} +z a^{-5} -a^2+ a^{-2} + a^{-4} }[/math] |
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