K12a820
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+9 q^5-16 q^4+22 q^3-26 q^2+28 q-25+21 q^{-1} -14 q^{-2} +8 q^{-3} -4 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-23 t^2+35 t-39+35 t^{-1} -23 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 179 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8+a^2 z^6-4 z^6 a^{-2} +z^6 a^{-4} -4 z^6+3 a^2 z^4-5 z^4 a^{-2} +3 z^4 a^{-4} -4 z^4+a^2 z^2-3 z^2 a^{-2} +2 z^2 a^{-4} +z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +6 a^2 z^{10}+9 z^{10} a^{-2} +15 z^{10}+4 a^3 z^9-a z^9+10 z^9 a^{-1} +15 z^9 a^{-3} +a^4 z^8-26 a^2 z^8-8 z^8 a^{-2} +18 z^8 a^{-4} -53 z^8-18 a^3 z^7-29 a z^7-50 z^7 a^{-1} -24 z^7 a^{-3} +15 z^7 a^{-5} -4 a^4 z^6+37 a^2 z^6-24 z^6 a^{-2} -32 z^6 a^{-4} +9 z^6 a^{-6} +58 z^6+25 a^3 z^5+48 a z^5+44 z^5 a^{-1} -3 z^5 a^{-3} -20 z^5 a^{-5} +4 z^5 a^{-7} +4 a^4 z^4-20 a^2 z^4+23 z^4 a^{-2} +17 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} -25 z^4-10 a^3 z^3-21 a z^3-9 z^3 a^{-1} +12 z^3 a^{-3} +9 z^3 a^{-5} -z^3 a^{-7} +3 a^2 z^2-6 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} +z^2-2 z a^{-1} -3 z a^{-3} -z a^{-5} +a^2+ a^{-2} +3 }[/math] |
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