K12n687
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-8+13 q^{-1} -16 q^{-2} +18 q^{-3} -17 q^{-4} +14 q^{-5} -9 q^{-6} +5 q^{-7} -2 q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-10 t^2+25 t-33+25 t^{-1} -10 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 107 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^8-z^4 a^6+a^6+z^6 a^4+2 z^4 a^4+2 z^2 a^4+z^6 a^2+2 z^4 a^2+2 z^2 a^2+a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^6 z^{10}+2 a^4 z^{10}+3 a^7 z^9+9 a^5 z^9+6 a^3 z^9+a^8 z^8-2 a^6 z^8+5 a^4 z^8+8 a^2 z^8-9 a^7 z^7-26 a^5 z^7-10 a^3 z^7+7 a z^7+2 a^8 z^6+a^6 z^6-19 a^4 z^6-14 a^2 z^6+4 z^6+3 a^9 z^5+18 a^7 z^5+35 a^5 z^5+8 a^3 z^5-11 a z^5+z^5 a^{-1} -9 a^8 z^4+22 a^4 z^4+7 a^2 z^4-6 z^4-8 a^9 z^3-20 a^7 z^3-18 a^5 z^3-3 a^3 z^3+2 a z^3-z^3 a^{-1} +5 a^8 z^2+a^6 z^2-6 a^4 z^2-a^2 z^2+z^2+4 a^9 z+6 a^7 z+3 a^5 z+a^3 z-a^8-a^6-a^2 }[/math] |
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