K12a602
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-11 q^5+19 q^4-28 q^3+34 q^2-36 q+34-27 q^{-1} +19 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+28 t^2-46 t+55-46 t^{-1} +28 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+2 z^4-z^2+1 }[/math] |
| Determinant | 229 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+3 z^6 a^{-2} -z^6 a^{-4} +4 z^6-3 a^2 z^4-2 z^4 a^{-4} +7 z^4-3 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} +8 z^2-a^2-5 a^{-2} +2 a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +18 z^{10} a^{-2} +9 z^{10} a^{-4} +9 z^{10}+14 a z^9+20 z^9 a^{-1} +16 z^9 a^{-3} +10 z^9 a^{-5} +14 a^2 z^8-34 z^8 a^{-2} -18 z^8 a^{-4} +5 z^8 a^{-6} +3 z^8+9 a^3 z^7-17 a z^7-59 z^7 a^{-1} -65 z^7 a^{-3} -31 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-22 a^2 z^6+z^6 a^{-2} -2 z^6 a^{-4} -14 z^6 a^{-6} -37 z^6+a^5 z^5-11 a^3 z^5+3 a z^5+49 z^5 a^{-1} +64 z^5 a^{-3} +28 z^5 a^{-5} -2 z^5 a^{-7} -4 a^4 z^4+18 a^2 z^4+27 z^4 a^{-2} +16 z^4 a^{-4} +9 z^4 a^{-6} +42 z^4-a^5 z^3+6 a^3 z^3+4 a z^3-17 z^3 a^{-1} -20 z^3 a^{-3} -6 z^3 a^{-5} +a^4 z^2-7 a^2 z^2-21 z^2 a^{-2} -7 z^2 a^{-4} -22 z^2-a^3 z-a z+z a^{-1} -z a^{-5} +a^2+5 a^{-2} +2 a^{-4} +5 }[/math] |
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