K12n525
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-6 q^3+12 q^2-16 q+19-20 q^{-1} +17 q^{-2} -13 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+8 t^2-28 t+43-28 t^{-1} +8 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+2 z^4-5 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-a^4+3 z^4 a^2+3 z^2 a^2+a^2-z^6-2 z^4-4 z^2-1+z^4 a^{-2} -z^2 a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+4 a^3 z^9+7 a z^9+3 z^9 a^{-1} +5 a^4 z^8+12 a^2 z^8+3 z^8 a^{-2} +10 z^8+3 a^5 z^7-a^3 z^7-a z^7+4 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-10 a^4 z^6-28 a^2 z^6+2 z^6 a^{-2} -15 z^6-7 a^5 z^5-11 a^3 z^5-18 a z^5-9 z^5 a^{-1} +5 z^5 a^{-3} -3 a^6 z^4+5 a^4 z^4+15 a^2 z^4-2 z^4 a^{-2} +3 z^4 a^{-4} +2 z^4+5 a^5 z^3+6 a^3 z^3+11 a z^3+6 z^3 a^{-1} -4 z^3 a^{-3} +3 a^6 z^2-2 a^2 z^2-z^2 a^{-2} -3 z^2 a^{-4} +3 z^2-a^5 z+a^3 z-2 z a^{-1} -a^6-a^4-a^2+ a^{-4} -1 }[/math] |
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