K12a528
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+15 q-21+27 q^{-1} -28 q^{-2} +27 q^{-3} -22 q^{-4} +15 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-21 t^2+39 t-47+39 t^{-1} -21 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+z^4+2 z^2+1 }[/math] |
| Determinant | 183 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-11 a^2 z^4-z^4 a^{-2} +7 z^4-2 a^6 z^2+8 a^4 z^2-10 a^2 z^2-2 z^2 a^{-2} +8 z^2-a^6+2 a^4-2 a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+8 a^2 z^{10}+4 z^{10}+8 a^5 z^9+16 a^3 z^9+14 a z^9+6 z^9 a^{-1} +10 a^6 z^8+13 a^4 z^8+4 z^8 a^{-2} +z^8+8 a^7 z^7-2 a^5 z^7-34 a^3 z^7-41 a z^7-16 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-14 a^6 z^6-43 a^4 z^6-43 a^2 z^6-13 z^6 a^{-2} -31 z^6+a^9 z^5-12 a^7 z^5-15 a^5 z^5+14 a^3 z^5+27 a z^5+8 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+9 a^6 z^4+41 a^4 z^4+53 a^2 z^4+13 z^4 a^{-2} +39 z^4-a^9 z^3+7 a^7 z^3+15 a^5 z^3+5 a^3 z^3-a z^3+4 z^3 a^{-1} +3 z^3 a^{-3} +a^8 z^2-4 a^6 z^2-16 a^4 z^2-23 a^2 z^2-5 z^2 a^{-2} -17 z^2-2 a^7 z-3 a^5 z-2 a^3 z-2 a z-2 z a^{-1} -z a^{-3} +a^6+2 a^4+2 a^2+ a^{-2} +3 }[/math] |
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