K12a334
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-12 q^3+21 q^2-31 q+38-39 q^{-1} +37 q^{-2} -29 q^{-3} +20 q^{-4} -11 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+28 t^2-54 t+67-54 t^{-1} +28 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^2+1 }[/math] |
| Determinant | 249 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-8 a^2 z^4-2 z^4 a^{-2} +7 z^4-a^6 z^2+5 a^4 z^2-5 a^2 z^2-z^2 a^{-2} +4 z^2-a^6+a^4+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+7 a^4 z^{10}+16 a^2 z^{10}+9 z^{10}+8 a^5 z^9+24 a^3 z^9+33 a z^9+17 z^9 a^{-1} +4 a^6 z^8-4 a^4 z^8-7 a^2 z^8+18 z^8 a^{-2} +19 z^8+a^7 z^7-21 a^5 z^7-75 a^3 z^7-79 a z^7-14 z^7 a^{-1} +12 z^7 a^{-3} -11 a^6 z^6-27 a^4 z^6-60 a^2 z^6-24 z^6 a^{-2} +5 z^6 a^{-4} -73 z^6-3 a^7 z^5+19 a^5 z^5+68 a^3 z^5+50 a z^5-10 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+36 a^4 z^4+68 a^2 z^4+13 z^4 a^{-2} -3 z^4 a^{-4} +59 z^4+3 a^7 z^3-8 a^5 z^3-27 a^3 z^3-13 a z^3+8 z^3 a^{-1} +5 z^3 a^{-3} -5 a^6 z^2-14 a^4 z^2-20 a^2 z^2-4 z^2 a^{-2} -15 z^2-a^7 z+2 a^5 z+6 a^3 z+4 a z+z a^{-1} +a^6+a^4-a^2 }[/math] |
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