K12n829
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q-4+8 q^{-1} -11 q^{-2} +15 q^{-3} -15 q^{-4} +14 q^{-5} -11 q^{-6} +7 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-11 t^2+18 t-21+18 t^{-1} -11 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-z^4+3 z^2+1 }[/math] |
| Determinant | 91 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8+a^6 z^6-5 a^4 z^6+a^2 z^6+3 a^6 z^4-7 a^4 z^4+3 a^2 z^4+a^6 z^2+2 a^2 z^2-2 a^6+3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{10}-2 z^4 a^{10}+4 z^7 a^9-11 z^5 a^9+6 z^3 a^9+6 z^8 a^8-17 z^6 a^8+12 z^4 a^8-2 z^2 a^8+4 z^9 a^7-5 z^7 a^7-9 z^5 a^7+13 z^3 a^7-4 z a^7+z^{10} a^6+7 z^8 a^6-22 z^6 a^6+18 z^4 a^6-6 z^2 a^6+2 a^6+5 z^9 a^5-6 z^7 a^5-3 z^5 a^5+9 z^3 a^5-5 z a^5+z^{10} a^4+z^8 a^4+4 z^6 a^4-7 z^4 a^4-z^2 a^4+3 a^4+z^9 a^3+3 z^7 a^3-z^5 a^3-z^3 a^3-z a^3+8 z^6 a^2-10 z^4 a^2+3 z^2 a^2+4 z^5 a-3 z^3 a+z^4 }[/math] |
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