K12a39
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+16 q-23+28 q^{-1} -29 q^{-2} +28 q^{-3} -22 q^{-4} +15 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-21 t^2+40 t-49+40 t^{-1} -21 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+z^4+3 z^2+1 }[/math] |
| Determinant | 187 |
| 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+8 a^4 z^4-12 a^2 z^4-z^4 a^{-2} +7 z^4-3 a^6 z^2+13 a^4 z^2-14 a^2 z^2-2 z^2 a^{-2} +9 z^2-3 a^6+7 a^4-6 a^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}+9 a^5 z^9+20 a^3 z^9+17 a z^9+6 z^9 a^{-1} +9 a^6 z^8+9 a^4 z^8+4 z^8 a^{-2} +4 z^8+6 a^7 z^7-11 a^5 z^7-53 a^3 z^7-52 a z^7-15 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-15 a^6 z^6-44 a^4 z^6-54 a^2 z^6-13 z^6 a^{-2} -41 z^6+a^9 z^5-8 a^7 z^5+3 a^5 z^5+43 a^3 z^5+41 a z^5+7 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+17 a^6 z^4+57 a^4 z^4+72 a^2 z^4+14 z^4 a^{-2} +50 z^4-2 a^9 z^3+5 a^7 z^3+7 a^5 z^3-10 a^3 z^3-10 a z^3+3 z^3 a^{-1} +3 z^3 a^{-3} +a^8 z^2-11 a^6 z^2-31 a^4 z^2-36 a^2 z^2-6 z^2 a^{-2} -23 z^2+a^9 z-2 a^7 z-4 a^5 z-a^3 z-a z-2 z a^{-1} -z a^{-3} +3 a^6+7 a^4+6 a^2+ a^{-2} +4 }[/math] |
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