K12n858
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q-4+10 q^{-1} -14 q^{-2} +18 q^{-3} -19 q^{-4} +17 q^{-5} -14 q^{-6} +9 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-11 t^2+26 t-33+26 t^{-1} -11 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+z^4+1 }[/math] |
| Determinant | 111 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-6 z^2 a^6-3 a^6+2 z^6 a^4+7 z^4 a^4+9 z^2 a^4+3 a^4-3 z^4 a^2-5 z^2 a^2-a^2+z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{10}-2 z^4 a^{10}+z^2 a^{10}+4 z^7 a^9-9 z^5 a^9+5 z^3 a^9-z a^9+7 z^8 a^8-16 z^6 a^8+8 z^4 a^8-3 z^2 a^8+a^8+6 z^9 a^7-9 z^7 a^7-4 z^5 a^7+3 z^3 a^7+2 z^{10} a^6+8 z^8 a^6-30 z^6 a^6+28 z^4 a^6-14 z^2 a^6+3 a^6+10 z^9 a^5-24 z^7 a^5+24 z^5 a^5-13 z^3 a^5+4 z a^5+2 z^{10} a^4+3 z^8 a^4-16 z^6 a^4+29 z^4 a^4-18 z^2 a^4+3 a^4+4 z^9 a^3-11 z^7 a^3+23 z^5 a^3-15 z^3 a^3+4 z a^3+2 z^8 a^2-3 z^6 a^2+12 z^4 a^2-10 z^2 a^2+a^2+4 z^5 a-4 z^3 a+z a+z^4-2 z^2+1 }[/math] |
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