K12a346
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-11 q^5+18 q^4-26 q^3+32 q^2-33 q+31-25 q^{-1} +17 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+27 t^2-42 t+49-42 t^{-1} +27 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+z^4-z^2+1 }[/math] |
| Determinant | 213 |
| 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} +6 z^4-2 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +5 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +17 z^{10} a^{-2} +9 z^{10} a^{-4} +8 z^{10}+11 a z^9+14 z^9 a^{-1} +13 z^9 a^{-3} +10 z^9 a^{-5} +11 a^2 z^8-39 z^8 a^{-2} -21 z^8 a^{-4} +5 z^8 a^{-6} -2 z^8+8 a^3 z^7-10 a z^7-44 z^7 a^{-1} -59 z^7 a^{-3} -32 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-13 a^2 z^6+20 z^6 a^{-2} +5 z^6 a^{-4} -14 z^6 a^{-6} -16 z^6+a^5 z^5-10 a^3 z^5-5 a z^5+34 z^5 a^{-1} +58 z^5 a^{-3} +28 z^5 a^{-5} -2 z^5 a^{-7} -5 a^4 z^4+4 a^2 z^4+7 z^4 a^{-2} +9 z^4 a^{-4} +8 z^4 a^{-6} +15 z^4-a^5 z^3+5 a^3 z^3+9 a z^3-5 z^3 a^{-1} -13 z^3 a^{-3} -5 z^3 a^{-5} +2 a^4 z^2+a^2 z^2-10 z^2 a^{-2} -4 z^2 a^{-4} -7 z^2-a^3 z-3 a z-3 z a^{-1} -2 z a^{-3} -z a^{-5} +2 a^{-2} + a^{-4} +2 }[/math] |
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