K12a1202
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+8 q^4-14 q^3+20 q^2-25 q+27-25 q^{-1} +20 q^{-2} -14 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 9 t^2-42 t+67-42 t^{-1} +9 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 9 z^4-6 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4+2 z^4 a^2-3 z^2 a^2-3 a^2+5 z^4+6 z^2+5+2 z^4 a^{-2} -3 z^2 a^{-2} -3 a^{-2} -3 z^2 a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+6 z^{10} a^{-2} +12 z^{10}+7 a^3 z^9+11 a z^9+11 z^9 a^{-1} +7 z^9 a^{-3} +5 a^4 z^8-11 a^2 z^8-11 z^8 a^{-2} +5 z^8 a^{-4} -32 z^8+3 a^5 z^7-17 a^3 z^7-56 a z^7-56 z^7 a^{-1} -17 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-9 a^4 z^6-9 z^6 a^{-4} +z^6 a^{-6} +20 z^6-7 a^5 z^5+18 a^3 z^5+93 a z^5+93 z^5 a^{-1} +18 z^5 a^{-3} -7 z^5 a^{-5} -3 a^6 z^4+17 a^2 z^4+17 z^4 a^{-2} -3 z^4 a^{-6} +28 z^4+3 a^5 z^3-18 a^3 z^3-57 a z^3-57 z^3 a^{-1} -18 z^3 a^{-3} +3 z^3 a^{-5} +3 a^6 z^2-15 a^2 z^2-15 z^2 a^{-2} +3 z^2 a^{-6} -24 z^2+6 a^3 z+12 a z+12 z a^{-1} +6 z a^{-3} -a^6+3 a^2+3 a^{-2} - a^{-6} +5 }[/math] |
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