K12n505
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q-6+10 q^{-1} -13 q^{-2} +17 q^{-3} -16 q^{-4} +14 q^{-5} -11 q^{-6} +6 q^{-7} -3 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-8 t^2+24 t-33+24 t^{-1} -8 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-2 z^4+z^2+1 }[/math] |
| Determinant | 99 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-2 z^4 a^6-4 z^2 a^6-4 a^6+z^6 a^4+3 z^4 a^4+7 z^2 a^4+5 a^4-3 z^4 a^2-5 z^2 a^2-2 a^2+2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^6 a^{10}-3 z^4 a^{10}+2 z^2 a^{10}+3 z^7 a^9-9 z^5 a^9+7 z^3 a^9-2 z a^9+4 z^8 a^8-9 z^6 a^8+3 z^4 a^8-z^2 a^8+a^8+4 z^9 a^7-8 z^7 a^7+2 z^5 a^7+3 z^3 a^7-4 z a^7+2 z^{10} a^6+z^8 a^6-12 z^6 a^6+16 z^4 a^6-10 z^2 a^6+4 a^6+9 z^9 a^5-28 z^7 a^5+38 z^5 a^5-19 z^3 a^5+z a^5+2 z^{10} a^4+z^8 a^4-10 z^6 a^4+19 z^4 a^4-12 z^2 a^4+5 a^4+5 z^9 a^3-16 z^7 a^3+32 z^5 a^3-25 z^3 a^3+5 z a^3+4 z^8 a^2-8 z^6 a^2+12 z^4 a^2-9 z^2 a^2+2 a^2+z^7 a+5 z^5 a-10 z^3 a+2 z a+3 z^4-4 z^2+1 }[/math] |
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