K12a89
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-7+14 q^{-1} -20 q^{-2} +25 q^{-3} -26 q^{-4} +25 q^{-5} -20 q^{-6} +14 q^{-7} -8 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-17 t^2+38 t-49+38 t^{-1} -17 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+7 z^4+6 z^2+1 }[/math] |
| Determinant | 167 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-2 a^8+z^6 a^6+2 z^4 a^6+3 z^2 a^6+2 a^6+2 z^6 a^4+5 z^4 a^4+4 z^2 a^4+z^6 a^2+2 z^4 a^2+3 z^2 a^2+2 a^2-z^4-2 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-10 z^6 a^{10}+10 z^4 a^{10}-3 z^2 a^{10}+5 z^9 a^9-15 z^7 a^9+14 z^5 a^9-7 z^3 a^9+3 z a^9+4 z^{10} a^8-5 z^8 a^8-7 z^6 a^8+5 z^4 a^8+3 z^2 a^8-2 a^8+z^{11} a^7+12 z^9 a^7-41 z^7 a^7+44 z^5 a^7-27 z^3 a^7+7 z a^7+8 z^{10} a^6-9 z^8 a^6-11 z^6 a^6+11 z^4 a^6-2 a^6+z^{11} a^5+14 z^9 a^5-37 z^7 a^5+34 z^5 a^5-15 z^3 a^5+2 z a^5+4 z^{10} a^4+6 z^8 a^4-25 z^6 a^4+24 z^4 a^4-6 z^2 a^4+7 z^9 a^3-7 z^7 a^3+2 z^5 a^3+2 z^3 a^3+7 z^8 a^2-8 z^6 a^2+3 z^4 a^2+3 z^2 a^2-2 a^2+5 z^7 a-5 z^5 a+z a+3 z^6-5 z^4+3 z^2-1+z^5 a^{-1} -2 z^3 a^{-1} +z a^{-1} }[/math] |
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