K12n839
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+5-9 q^{-1} +14 q^{-2} -18 q^{-3} +20 q^{-4} -19 q^{-5} +16 q^{-6} -11 q^{-7} +6 q^{-8} -2 q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+18 t^2-23 t+23-23 t^{-1} +18 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-4 z^4+2 z^2+1 }[/math] |
| Determinant | 121 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+z^4 a^8+4 z^2 a^8+2 a^8-2 z^6 a^6-7 z^4 a^6-5 z^2 a^6-a^6+z^8 a^4+4 z^6 a^4+4 z^4 a^4+z^2 a^4-a^4-z^6 a^2-2 z^4 a^2+2 z^2 a^2+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^3 a^{11}-z a^{11}+z^6 a^{10}+6 z^4 a^{10}-4 z^2 a^{10}+a^{10}+4 z^7 a^9+z^5 a^9-3 z^3 a^9+2 z a^9+8 z^8 a^8-15 z^6 a^8+16 z^4 a^8-10 z^2 a^8+2 a^8+9 z^9 a^7-24 z^7 a^7+31 z^5 a^7-25 z^3 a^7+6 z a^7+4 z^{10} a^6+z^8 a^6-26 z^6 a^6+27 z^4 a^6-11 z^2 a^6+a^6+17 z^9 a^5-57 z^7 a^5+58 z^5 a^5-25 z^3 a^5+4 z a^5+4 z^{10} a^4-2 z^8 a^4-26 z^6 a^4+28 z^4 a^4-3 z^2 a^4-a^4+8 z^9 a^3-28 z^7 a^3+26 z^5 a^3-6 z^3 a^3+z a^3+5 z^8 a^2-16 z^6 a^2+11 z^4 a^2+2 z^2 a^2-2 a^2+z^7 a-2 z^5 a }[/math] |
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