K12a104
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-7+13 q^{-1} -18 q^{-2} +24 q^{-3} -25 q^{-4} +24 q^{-5} -20 q^{-6} +14 q^{-7} -9 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-17 t^2+37 t-47+37 t^{-1} -17 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+7 z^4+5 z^2+1 }[/math] |
| Determinant | 163 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8+z^6 a^6+z^4 a^6-2 z^2 a^6-3 a^6+2 z^6 a^4+6 z^4 a^4+8 z^2 a^4+4 a^4+z^6 a^2+2 z^4 a^2+2 z^2 a^2+a^2-z^4-2 z^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-13 z^6 a^{10}+12 z^4 a^{10}-3 z^2 a^{10}+6 z^9 a^9-17 z^7 a^9+10 z^5 a^9+2 z^3 a^9-z a^9+4 z^{10} a^8-2 z^8 a^8-20 z^6 a^8+21 z^4 a^8-4 z^2 a^8+z^{11} a^7+11 z^9 a^7-32 z^7 a^7+15 z^5 a^7+8 z^3 a^7-6 z a^7+7 z^{10} a^6-4 z^8 a^6-23 z^6 a^6+26 z^4 a^6-11 z^2 a^6+3 a^6+z^{11} a^5+10 z^9 a^5-17 z^7 a^5-6 z^5 a^5+21 z^3 a^5-10 z a^5+3 z^{10} a^4+8 z^8 a^4-24 z^6 a^4+22 z^4 a^4-11 z^2 a^4+4 a^4+5 z^9 a^3+2 z^7 a^3-15 z^5 a^3+16 z^3 a^3-5 z a^3+6 z^8 a^2-5 z^6 a^2+2 z^2 a^2-a^2+5 z^7 a-6 z^5 a+2 z^3 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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