K12a41
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-7 q^{-1} +14 q^{-2} -20 q^{-3} +27 q^{-4} -29 q^{-5} +28 q^{-6} -24 q^{-7} +17 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+23 t^2-37 t+43-37 t^{-1} +23 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+9 z^4+6 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-3 z^2 a^8-a^8+z^8 a^6+4 z^6 a^6+5 z^4 a^6+z^2 a^6-2 a^6+z^8 a^4+5 z^6 a^4+11 z^4 a^4+13 z^2 a^4+6 a^4-z^6 a^2-4 z^4 a^2-5 z^2 a^2-2 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}+10 z^4 a^{10}-3 z^2 a^{10}+10 z^9 a^9-6 z^7 a^9-11 z^5 a^9+11 z^3 a^9-2 z a^9+5 z^{10} a^8+10 z^8 a^8-32 z^6 a^8+20 z^4 a^8-2 z^2 a^8-a^8+z^{11} a^7+17 z^9 a^7-35 z^7 a^7+16 z^5 a^7+z^3 a^7-2 z a^7+8 z^{10} a^6-3 z^8 a^6-26 z^6 a^6+28 z^4 a^6-11 z^2 a^6+2 a^6+z^{11} a^5+11 z^9 a^5-30 z^7 a^5+17 z^5 a^5+5 z^3 a^5-6 z a^5+3 z^{10} a^4+2 z^8 a^4-26 z^6 a^4+36 z^4 a^4-21 z^2 a^4+6 a^4+4 z^9 a^3-9 z^7 a^3+10 z^3 a^3-5 z a^3+3 z^8 a^2-11 z^6 a^2+14 z^4 a^2-8 z^2 a^2+2 a^2+z^7 a-4 z^5 a+5 z^3 a-2 z a }[/math] |
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