K12a1271
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+16 q-22+28 q^{-1} -30 q^{-2} +28 q^{-3} -23 q^{-4} +16 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-20 t^2+44 t-55+44 t^{-1} -20 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+4 z^4+1 }[/math] |
| Determinant | 191 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-z^2 a^6+z^6 a^4+z^4 a^4+2 z^6 a^2+4 z^4 a^2+2 z^2 a^2+z^6+z^4+1-z^4 a^{-2} -z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+9 a^4 z^{10}+16 a^2 z^{10}+7 z^{10}+12 a^5 z^9+11 a^3 z^9+6 a z^9+7 z^9 a^{-1} +11 a^6 z^8-16 a^4 z^8-49 a^2 z^8+4 z^8 a^{-2} -18 z^8+8 a^7 z^7-24 a^5 z^7-52 a^3 z^7-43 a z^7-22 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-17 a^6 z^6+11 a^4 z^6+54 a^2 z^6-13 z^6 a^{-2} +9 z^6+a^9 z^5-11 a^7 z^5+23 a^5 z^5+71 a^3 z^5+58 a z^5+19 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+8 a^6 z^4-a^4 z^4-25 a^2 z^4+11 z^4 a^{-2} -a^9 z^3+3 a^7 z^3-11 a^5 z^3-37 a^3 z^3-32 a z^3-8 z^3 a^{-1} +2 z^3 a^{-3} +a^8 z^2-a^6 z^2+4 a^2 z^2-3 z^2 a^{-2} -z^2+2 a^5 z+6 a^3 z+6 a z+2 z a^{-1} +1 }[/math] |
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