K12a203
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-8 q^2+15 q-21+26 q^{-1} -29 q^{-2} +27 q^{-3} -22 q^{-4} +16 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-22 t^2+39 t-45+39 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 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^4-12 a^2 z^4-z^4 a^{-2} +7 z^4-2 a^6 z^2+9 a^4 z^2-15 a^2 z^2-2 z^2 a^{-2} +8 z^2-a^6+5 a^4-7 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+16 a z^9+6 z^9 a^{-1} +11 a^6 z^8+10 a^4 z^8-4 a^2 z^8+4 z^8 a^{-2} +z^8+8 a^7 z^7-13 a^5 z^7-59 a^3 z^7-57 a z^7-18 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-18 a^6 z^6-49 a^4 z^6-49 a^2 z^6-14 z^6 a^{-2} -36 z^6+a^9 z^5-11 a^7 z^5+4 a^5 z^5+60 a^3 z^5+62 a z^5+15 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+13 a^6 z^4+62 a^4 z^4+81 a^2 z^4+15 z^4 a^{-2} +52 z^4-a^9 z^3+4 a^7 z^3+2 a^5 z^3-25 a^3 z^3-30 a z^3-6 z^3 a^{-1} +2 z^3 a^{-3} +a^8 z^2-6 a^6 z^2-31 a^4 z^2-45 a^2 z^2-6 z^2 a^{-2} -27 z^2-a^7 z-a^5 z+5 a^3 z+7 a z+2 z a^{-1} +a^6+5 a^4+7 a^2+4 }[/math] |
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