K12a565
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-8 q^{-1} +15 q^{-2} -22 q^{-3} +28 q^{-4} -30 q^{-5} +29 q^{-6} -24 q^{-7} +17 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+23 t^2-41 t+49-41 t^{-1} +23 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+z^4+4 z^2+1 }[/math] |
| Determinant | 193 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-a^{10}+3 z^4 a^8+6 z^2 a^8+2 a^8-3 z^6 a^6-10 z^4 a^6-10 z^2 a^6-3 a^6+z^8 a^4+5 z^6 a^4+11 z^4 a^4+11 z^2 a^4+3 a^4-z^6 a^2-3 z^4 a^2-2 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+9 z^7 a^{11}-13 z^5 a^{11}+9 z^3 a^{11}-3 z a^{11}+12 z^8 a^{10}-17 z^6 a^{10}+11 z^4 a^{10}-5 z^2 a^{10}+a^{10}+10 z^9 a^9-5 z^7 a^9-13 z^5 a^9+12 z^3 a^9-2 z a^9+5 z^{10} a^8+13 z^8 a^8-44 z^6 a^8+38 z^4 a^8-14 z^2 a^8+2 a^8+z^{11} a^7+20 z^9 a^7-47 z^7 a^7+34 z^5 a^7-12 z^3 a^7+2 z a^7+9 z^{10} a^6-2 z^8 a^6-41 z^6 a^6+52 z^4 a^6-23 z^2 a^6+3 a^6+z^{11} a^5+16 z^9 a^5-52 z^7 a^5+52 z^5 a^5-21 z^3 a^5+2 z a^5+4 z^{10} a^4+z^8 a^4-32 z^6 a^4+44 z^4 a^4-20 z^2 a^4+3 a^4+6 z^9 a^3-18 z^7 a^3+16 z^5 a^3-5 z^3 a^3+z a^3+4 z^8 a^2-14 z^6 a^2+15 z^4 a^2-5 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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