K12n846
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+5 q^4-7 q^3+11 q^2-13 q+13-12 q^{-1} +9 q^{-2} -5 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^2-20 t+31-20 t^{-1} +5 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^4+1 }[/math] |
| Determinant | 81 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^4+z^4 a^2+a^2+2 z^4-2+2 z^4 a^{-2} +3 z^2 a^{-2} +3 a^{-2} -2 z^2 a^{-4} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+4 a z^9+7 z^9 a^{-1} +3 z^9 a^{-3} +4 a^2 z^8-7 z^8 a^{-2} +z^8 a^{-4} -4 z^8+4 a^3 z^7-12 a z^7-28 z^7 a^{-1} -12 z^7 a^{-3} +3 a^4 z^6-7 a^2 z^6+17 z^6 a^{-2} +2 z^6 a^{-4} +5 z^6+a^5 z^5-8 a^3 z^5+19 a z^5+49 z^5 a^{-1} +24 z^5 a^{-3} +3 z^5 a^{-5} -7 a^4 z^4+2 a^2 z^4-24 z^4 a^{-2} -13 z^4 a^{-4} -2 z^4-2 a^5 z^3+3 a^3 z^3-10 a z^3-32 z^3 a^{-1} -25 z^3 a^{-3} -8 z^3 a^{-5} +3 a^4 z^2+3 a^2 z^2+16 z^2 a^{-2} +10 z^2 a^{-4} +6 z^2+a z+5 z a^{-1} +7 z a^{-3} +3 z a^{-5} -a^2-3 a^{-2} - a^{-4} -2 }[/math] |
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