K12n569
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^2+5 q-8+12 q^{-1} -13 q^{-2} +14 q^{-3} -12 q^{-4} +9 q^{-5} -5 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-10 t^2+18 t-21+18 t^{-1} -10 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 83 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-3 z^2 a^6-2 a^6+z^6 a^4+3 z^4 a^4+3 z^2 a^4+a^4+2 z^6 a^2+8 z^4 a^2+10 z^2 a^2+4 a^2-2 z^4-5 z^2-2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+3 a^5 z^9+5 a^3 z^9+2 a z^9+4 a^6 z^8+4 a^4 z^8+a^2 z^8+z^8+3 a^7 z^7-5 a^5 z^7-12 a^3 z^7-4 a z^7+2 a^8 z^6-10 a^6 z^6-15 a^4 z^6-a^2 z^6+2 z^6+a^9 z^5-5 a^7 z^5+4 a^5 z^5+15 a^3 z^5+8 a z^5+3 z^5 a^{-1} -4 a^8 z^4+15 a^6 z^4+22 a^4 z^4-7 a^2 z^4-10 z^4-3 a^9 z^3+2 a^7 z^3+4 a^5 z^3-9 a^3 z^3-15 a z^3-7 z^3 a^{-1} +a^8 z^2-10 a^6 z^2-9 a^4 z^2+9 a^2 z^2+7 z^2+2 a^9 z-a^7 z-3 a^5 z+3 a^3 z+6 a z+3 z a^{-1} +2 a^6+a^4-4 a^2-2 }[/math] |
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