K12a327
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-7+14 q^{-1} -20 q^{-2} +26 q^{-3} -27 q^{-4} +26 q^{-5} -22 q^{-6} +15 q^{-7} -9 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-18 t^2+40 t-51+40 t^{-1} -18 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+6 z^4+4 z^2+1 }[/math] |
| Determinant | 175 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8+z^6 a^6+z^4 a^6-z^2 a^6-2 a^6+2 z^6 a^4+5 z^4 a^4+5 z^2 a^4+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}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-13 z^6 a^{10}+13 z^4 a^{10}-4 z^2 a^{10}+6 z^9 a^9-16 z^7 a^9+9 z^5 a^9+2 z^3 a^9-2 z a^9+4 z^{10} a^8+z^8 a^8-29 z^6 a^8+30 z^4 a^8-8 z^2 a^8+z^{11} a^7+14 z^9 a^7-41 z^7 a^7+24 z^5 a^7+4 z^3 a^7-6 z a^7+8 z^{10} a^6-2 z^8 a^6-37 z^6 a^6+42 z^4 a^6-15 z^2 a^6+2 a^6+z^{11} a^5+15 z^9 a^5-35 z^7 a^5+17 z^5 a^5+9 z^3 a^5-7 z a^5+4 z^{10} a^4+8 z^8 a^4-32 z^6 a^4+34 z^4 a^4-13 z^2 a^4+2 a^4+7 z^9 a^3-6 z^7 a^3-z^5 a^3+6 z^3 a^3-2 z a^3+7 z^8 a^2-8 z^6 a^2+4 z^4 a^2+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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