K12a92
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-8 q^2+15 q-21+28 q^{-1} -30 q^{-2} +29 q^{-3} -24 q^{-4} +17 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-23 t^2+40 t-47+40 t^{-1} -23 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+5 z^4+4 z^2+1 }[/math] |
| Determinant | 191 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-6 a^2 z^4-z^4 a^{-2} +7 z^4-2 a^6 z^2+5 a^4 z^2-4 a^2 z^2-3 z^2 a^{-2} +8 z^2-a^6+a^4-a^2-2 a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+5 a^4 z^{10}+9 a^2 z^{10}+4 z^{10}+10 a^5 z^9+20 a^3 z^9+15 a z^9+5 z^9 a^{-1} +12 a^6 z^8+13 a^4 z^8-4 a^2 z^8+3 z^8 a^{-2} -2 z^8+9 a^7 z^7-5 a^5 z^7-48 a^3 z^7-49 a z^7-14 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-17 a^6 z^6-44 a^4 z^6-32 a^2 z^6-10 z^6 a^{-2} -19 z^6+a^9 z^5-13 a^7 z^5-13 a^5 z^5+37 a^3 z^5+51 a z^5+11 z^5 a^{-1} -4 z^5 a^{-3} -4 a^8 z^4+11 a^6 z^4+37 a^4 z^4+38 a^2 z^4+11 z^4 a^{-2} +27 z^4-a^9 z^3+9 a^7 z^3+12 a^5 z^3-15 a^3 z^3-24 a z^3-2 z^3 a^{-1} +5 z^3 a^{-3} +a^8 z^2-5 a^6 z^2-12 a^4 z^2-14 a^2 z^2-6 z^2 a^{-2} -14 z^2-3 a^7 z-2 a^5 z+4 a^3 z+4 a z-z a^{-1} -2 z a^{-3} +a^6+a^4+a^2+2 a^{-2} +4 }[/math] |
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