K12a423
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+11 q-14+18 q^{-1} -18 q^{-2} +17 q^{-3} -13 q^{-4} +9 q^{-5} -5 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-14 t^2+26 t-31+26 t^{-1} -14 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+10 z^4+6 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-3 z^2 a^6-2 a^6+z^6 a^4+3 z^4 a^4+3 z^2 a^4+a^4+2 z^6 a^2+7 z^4 a^2+8 z^2 a^2+3 a^2+z^6+2 z^4-z^4 a^{-2} -2 z^2 a^{-2} - a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+4 a^5 z^9+5 a^3 z^9+5 a z^9+4 z^9 a^{-1} +4 a^6 z^8-5 a^4 z^8-17 a^2 z^8+3 z^8 a^{-2} -5 z^8+3 a^7 z^7-9 a^5 z^7-24 a^3 z^7-25 a z^7-12 z^7 a^{-1} +z^7 a^{-3} +2 a^8 z^6-9 a^6 z^6+a^4 z^6+16 a^2 z^6-11 z^6 a^{-2} -7 z^6+a^9 z^5-5 a^7 z^5+11 a^5 z^5+39 a^3 z^5+32 a z^5+6 z^5 a^{-1} -4 z^5 a^{-3} -4 a^8 z^4+12 a^6 z^4+10 a^4 z^4-8 a^2 z^4+11 z^4 a^{-2} +9 z^4-3 a^9 z^3+2 a^7 z^3-2 a^5 z^3-26 a^3 z^3-23 a z^3+z^3 a^{-1} +5 z^3 a^{-3} +a^8 z^2-8 a^6 z^2-6 a^4 z^2+5 a^2 z^2-4 z^2 a^{-2} -2 z^2+2 a^9 z-a^7 z-a^5 z+7 a^3 z+7 a z-2 z a^{-3} +2 a^6+a^4-3 a^2+ a^{-2} }[/math] |
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