K12a155
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+14 q^5-20 q^4+25 q^3-27 q^2+25 q-21+15 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-15 t^2+41 t-55+41 t^{-1} -15 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^4-z^2+1 }[/math] |
| Determinant | 171 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-a^2 z^4-z^4 a^{-2} -3 z^4 a^{-4} +2 z^4-a^2 z^2-5 z^2 a^{-2} -2 z^2 a^{-4} +3 z^2 a^{-6} +4 z^2-4 a^{-2} + a^{-4} +2 a^{-6} - a^{-8} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +4 z^{10} a^{-4} +4 z^{10}+6 a z^9+14 z^9 a^{-1} +15 z^9 a^{-3} +7 z^9 a^{-5} +4 a^2 z^8-4 z^8 a^{-2} +7 z^8 a^{-4} +7 z^8 a^{-6} +a^3 z^7-18 a z^7-48 z^7 a^{-1} -41 z^7 a^{-3} -7 z^7 a^{-5} +5 z^7 a^{-7} -14 a^2 z^6-36 z^6 a^{-2} -30 z^6 a^{-4} -8 z^6 a^{-6} +3 z^6 a^{-8} -31 z^6-3 a^3 z^5+15 a z^5+50 z^5 a^{-1} +41 z^5 a^{-3} +3 z^5 a^{-5} -5 z^5 a^{-7} +z^5 a^{-9} +15 a^2 z^4+55 z^4 a^{-2} +34 z^4 a^{-4} +3 z^4 a^{-6} -5 z^4 a^{-8} +44 z^4+2 a^3 z^3-5 a z^3-28 z^3 a^{-1} -24 z^3 a^{-3} -z^3 a^{-5} -2 z^3 a^{-9} -5 a^2 z^2-31 z^2 a^{-2} -14 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2 a^{-8} -22 z^2+2 a z+8 z a^{-1} +8 z a^{-3} +2 z a^{-5} +z a^{-7} +z a^{-9} +4 a^{-2} + a^{-4} -2 a^{-6} - a^{-8} +3 }[/math] |
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