K12a849
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+16 q^{-1} -22 q^{-2} +28 q^{-3} -29 q^{-4} +27 q^{-5} -22 q^{-6} +15 q^{-7} -9 q^{-8} +4 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-19 t^2+43 t-55+43 t^{-1} -19 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+5 z^4+3 z^2+1 }[/math] |
| Determinant | 187 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-z^2 a^8+z^6 a^6+z^4 a^6-z^2 a^6-2 a^6+2 z^6 a^4+5 z^4 a^4+6 z^2 a^4+3 a^4+z^6 a^2+z^4 a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-3 z^5 a^{11}+2 z^3 a^{11}+4 z^8 a^{10}-13 z^6 a^{10}+11 z^4 a^{10}-2 z^2 a^{10}+7 z^9 a^9-23 z^7 a^9+23 z^5 a^9-10 z^3 a^9+2 z a^9+6 z^{10} a^8-13 z^8 a^8+2 z^6 a^8+4 z^4 a^8-z^2 a^8+2 z^{11} a^7+10 z^9 a^7-43 z^7 a^7+46 z^5 a^7-19 z^3 a^7+z a^7+12 z^{10} a^6-25 z^8 a^6+8 z^6 a^6+10 z^4 a^6-8 z^2 a^6+2 a^6+2 z^{11} a^5+13 z^9 a^5-39 z^7 a^5+32 z^5 a^5-5 z^3 a^5-2 z a^5+6 z^{10} a^4+3 z^8 a^4-29 z^6 a^4+35 z^4 a^4-15 z^2 a^4+3 a^4+10 z^9 a^3-12 z^7 a^3+7 z^3 a^3-2 z a^3+11 z^8 a^2-18 z^6 a^2+13 z^4 a^2-5 z^2 a^2+8 z^7 a-11 z^5 a+4 z^3 a-z a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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