K12n802
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+14 q^2-18 q+21-19 q^{-1} +16 q^{-2} -11 q^{-3} +6 q^{-4} -2 q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+14 t^2-25 t+31-25 t^{-1} +14 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+4 z^4+2 z^2+1 }[/math] |
| Determinant | 121 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +5 z^6-2 a^2 z^4-3 z^4 a^{-2} +9 z^4-a^4 z^2-3 z^2 a^{-2} +6 z^2-a^4+a^2- a^{-2} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+3 a^3 z^9+10 a z^9+7 z^9 a^{-1} +a^4 z^8+a^2 z^8+10 z^8 a^{-2} +10 z^8-5 a^3 z^7-22 a z^7-9 z^7 a^{-1} +8 z^7 a^{-3} +4 a^4 z^6-2 a^2 z^6-20 z^6 a^{-2} +4 z^6 a^{-4} -30 z^6+3 a^5 z^5+10 a^3 z^5+24 a z^5+3 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} -11 a^4 z^4-3 a^2 z^4+17 z^4 a^{-2} -5 z^4 a^{-4} +30 z^4-6 a^5 z^3-16 a^3 z^3-15 a z^3+z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} +5 a^4 z^2+2 a^2 z^2-7 z^2 a^{-2} -10 z^2+3 a^5 z+6 a^3 z+4 a z-z a^{-3} -a^4-a^2+ a^{-2} +2 }[/math] |
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