K12a566
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-8+14 q^{-1} -19 q^{-2} +23 q^{-3} -24 q^{-4} +22 q^{-5} -17 q^{-6} +12 q^{-7} -7 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+37 t-51+37 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4+3 z^2+1 }[/math] |
| Determinant | 155 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+3 z^2 a^8+2 a^8-3 z^4 a^6-4 z^2 a^6-2 a^6+z^6 a^4+z^4 a^4+2 z^2 a^4+a^4+z^6 a^2+2 z^4 a^2+3 z^2 a^2+a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+3 z^8 a^{10}-11 z^6 a^{10}+11 z^4 a^{10}-5 z^2 a^{10}+a^{10}+5 z^9 a^9-18 z^7 a^9+20 z^5 a^9-12 z^3 a^9+4 z a^9+4 z^{10} a^8-8 z^8 a^8-6 z^6 a^8+17 z^4 a^8-10 z^2 a^8+2 a^8+z^{11} a^7+11 z^9 a^7-50 z^7 a^7+72 z^5 a^7-45 z^3 a^7+10 z a^7+8 z^{10} a^6-16 z^8 a^6-z^6 a^6+21 z^4 a^6-13 z^2 a^6+2 a^6+z^{11} a^5+13 z^9 a^5-45 z^7 a^5+60 z^5 a^5-35 z^3 a^5+7 z a^5+4 z^{10} a^4+3 z^8 a^4-19 z^6 a^4+20 z^4 a^4-7 z^2 a^4+a^4+7 z^9 a^3-7 z^7 a^3+z^5 a^3-2 z^3 a^3+2 z a^3+8 z^8 a^2-9 z^6 a^2-z^4 a^2+3 z^2 a^2-a^2+7 z^7 a-10 z^5 a+3 z^3 a+4 z^6-6 z^4+2 z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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